CINXE.COM
About: Baker's theorem
<!DOCTYPE html> <html prefix=" dbp: http://dbpedia.org/property/ dbo: http://dbedia.org/ontology/ dct: http://purl.org/dc/terms/ dbd: http://dbpedia.org/datatype/ og: https://ogp.me/ns# " > <!-- header --> <head> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>About: Baker's theorem</title> <!-- Links --> <link rel="alternate" type="application/rdf+xml" href="http://dbpedia.org/data/Baker's_theorem.rdf" title="Structured Descriptor Document (RDF/XML format)" /> <link rel="alternate" type="text/n3" href="http://dbpedia.org/data/Baker's_theorem.n3" title="Structured Descriptor Document (N3 format)" /> <link rel="alternate" type="text/turtle" href="http://dbpedia.org/data/Baker's_theorem.ttl" title="Structured Descriptor Document (Turtle format)" /> <link rel="alternate" type="application/json+rdf" href="http://dbpedia.org/data/Baker's_theorem.jrdf" title="Structured Descriptor Document (RDF/JSON format)" /> <link rel="alternate" type="application/json" href="http://dbpedia.org/data/Baker's_theorem.json" title="Structured Descriptor Document (RDF/JSON format)" /> <link rel="alternate" type="application/atom+xml" href="http://dbpedia.org/data/Baker's_theorem.atom" title="OData (Atom+Feed format)" /> <link rel="alternate" type="text/plain" href="http://dbpedia.org/data/Baker's_theorem.ntriples" title="Structured Descriptor Document (N-Triples format)" /> <link rel="alternate" type="text/csv" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fcsv" title="Structured Descriptor Document (CSV format)" /> <link rel="alternate" type="application/microdata+json" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=application%2Fmicrodata%2Bjson" title="Structured Descriptor Document (Microdata/JSON format)" /> <link rel="alternate" type="text/html" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fhtml" title="Structured Descriptor Document (Microdata/HTML format)" /> <link rel="alternate" type="application/ld+json" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=application%2Fld%2Bjson" title="Structured Descriptor Document (JSON-LD format)" /> <link rel="alternate" type="text/x-html-script-ld+json" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fx-html-script-ld%2Bjson" title="Structured Descriptor Document (HTML with embedded JSON-LD)" /> <link rel="alternate" type="text/x-html-script-turtle" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fx-html-script-turtle" title="Structured Descriptor Document (HTML with embedded Turtle)" /> <link rel="timegate" type="text/html" href="http://dbpedia.mementodepot.org/timegate/http://dbpedia.org/page/Baker's_theorem" title="Time Machine" /> <link rel="foaf:primarytopic" href="http://dbpedia.org/resource/Baker's_theorem"/> <link rev="describedby" href="http://dbpedia.org/resource/Baker's_theorem"/> <!-- /Links --> <!-- Stylesheets --> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap/5.2.1/css/bootstrap.min.css" integrity="sha512-siwe/oXMhSjGCwLn+scraPOWrJxHlUgMBMZXdPe2Tnk3I0x3ESCoLz7WZ5NTH6SZrywMY+PB1cjyqJ5jAluCOg==" crossorigin="anonymous" /> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-icons/1.9.1/font/bootstrap-icons.min.css" integrity="sha512-5PV92qsds/16vyYIJo3T/As4m2d8b6oWYfoqV+vtizRB6KhF1F9kYzWzQmsO6T3z3QG2Xdhrx7FQ+5R1LiQdUA==" crossorigin="anonymous" /> <!-- link rel="stylesheet" href="/statics/css/dbpedia.css" --> <!-- /Stylesheets--> <!-- OpenGraph --> <meta property="og:title" content="Baker's theorem" /> <meta property="og:type" content="article" /> <meta property="og:url" content="http://dbpedia.org/resource/Baker's_theorem" /> <meta property="og:image" content="/statics/images/dbpedia_logo.png" /> <meta property="og:description" content="In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. The result, proved by Alan Baker , subsumed many earlier results in transcendental number theory and solved a problem posed by Alexander Gelfond nearly fifteen years earlier.Baker used this to prove the transcendence of many numbers, to derive effective bounds for the solutions of some Diophantine equations, and to solve the class number problem of finding all imaginary quadratic fields with class number 1." /> <meta property="og:site_name" content="DBpedia" /> <!-- /OpenGraph--> </head> <body about="http://dbpedia.org/resource/Baker's_theorem"> <!-- navbar --> <nav class="navbar navbar-expand-md navbar-light bg-light fixed-top align-items-center"> <div class="container-xl"> <a class="navbar-brand" href="http://wiki.dbpedia.org/about" title="About DBpedia" style="color: #2c5078"> <img class="img-fluid" src="/statics/images/dbpedia_logo_land_120.png" alt="About DBpedia" /> </a> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#dbp-navbar" aria-controls="dbp-navbar" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="collapse navbar-collapse" id="dbp-navbar"> <ul class="navbar-nav me-auto mb-2 mb-lg-0"> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownBrowse" role="button" data-bs-toggle="dropdown" aria-expanded="false"> <i class="bi-eye-fill"></i> Browse using<span class="caret"></span></a> <ul class="dropdown-menu" aria-labelledby="navbarDropdownBrowse"> <li class="dropdown-item"><a class="nav-link" href="/describe/?uri=http%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem">OpenLink Faceted Browser</a></li> <li class="dropdown-item"><a class="nav-link" href="http://osde.demo.openlinksw.com/#/editor?uri=http%3A%2F%2Fdbpedia.org%2Fdata%2FBaker%27s_theorem.ttl&view=statements">OpenLink Structured Data Editor</a></li> <li class="dropdown-item"><a class="nav-link" href="http://en.lodlive.it/?http%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem">LodLive Browser</a></li> <!-- li class="dropdown-item"><a class="nav-link" href="http://lodmilla.sztaki.hu/lodmilla/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem">LODmilla Browser</a></li --> </ul> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownFormats" role="button" data-bs-toggle="dropdown" aria-expanded="false"> <i class="bi-file-earmark-fill"></i> Formats<span class="caret"></span></a> <ul class="dropdown-menu" aria-labelledby="navbarDropdownFormats"> <li class="dropdown-item-text">RDF:</li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Baker's_theorem.ntriples">N-Triples</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Baker's_theorem.n3">N3</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Baker's_theorem.ttl">Turtle</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Baker's_theorem.json">JSON</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Baker's_theorem.rdf">XML</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">OData:</li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Baker's_theorem.atom">Atom</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Baker's_theorem.jsod">JSON</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">Microdata:</li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=application%2Fmicrodata%2Bjson">JSON</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fhtml">HTML</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">Embedded:</li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fx-html-script-ld%2Bjson">JSON</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fx-html-script-turtle">Turtle</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">Other:</li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=text%2Fcsv">CSV</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FBaker%27s_theorem%3E&format=application%2Fld%2Bjson">JSON-LD</a></li> </ul> </li> </ul> <ul class="navbar-nav ms-auto"> <li class="nav-item"> <a class="nav-link" href="/fct/" title="Switch to /fct endpoint"><i class="bi-box-arrow-up-right"></i> Faceted Browser </a> </li> <li class="nav-item"> <a class="nav-link" href="/sparql/" title="Switch to /sparql endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div> <!-- /navbar --> <!-- page-header --> <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/Baker's_theorem">Baker's theorem</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/class/yago/WikicatTheoremsInNumberTheory">WikicatTheoremsInNumberTheory</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. The result, proved by Alan Baker , subsumed many earlier results in transcendental number theory and solved a problem posed by Alexander Gelfond nearly fifteen years earlier.Baker used this to prove the transcendence of many numbers, to derive effective bounds for the solutions of some Diophantine equations, and to solve the class number problem of finding all imaginary quadratic fields with class number 1.</p> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ar" >تدخل مبرهنة باكر في إطار نظرية الأعداد المتسامية، ونعطي أدنى حد لقيمة مطلقة من التركيبات الخطية من لوغاريتمات الأعداد الجبرية. سميت هذه المبرهنة هكذا نسبة إلى آلان باكر.</span><small> (ar)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. The result, proved by Alan Baker , subsumed many earlier results in transcendental number theory and solved a problem posed by Alexander Gelfond nearly fifteen years earlier.Baker used this to prove the transcendence of many numbers, to derive effective bounds for the solutions of some Diophantine equations, and to solve the class number problem of finding all imaginary quadratic fields with class number 1.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >Le théorème de Baker résout la conjecture de Gelfond. Publié par Alan Baker en 1966 et 1967, c'est un résultat de transcendance sur les logarithmes de nombres algébriques, qui généralise à la fois le théorème d'Hermite-Lindemann (1882) et le théorème de Gelfond-Schneider (1934). Ce théorème a été adapté au cas des nombres p-adiques par ; le permet de démontrer la conjecture de Leopoldt dans le cas d'un corps de nombres abélien, suivant un article d'Ax.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ja" >ベイカーの定理（ベイカーのていり、英: Baker's theorem）とは、1966年-1968年にかけて、アラン・ベイカーによって発表された、対数関数の一次形式に対する線形独立性、および下界の評価に関する一連の定理のことである。下界の評価が計算可能であることから、数論の様々な分野で応用されている。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="nl" >In de transcendentietheorie, een deelgebied van de wiskunde, geeft de stelling van Baker een ondergrens voor lineaire combinaties van logaritmen van algebraïsche getallen. De stelling is bewezen door en vernoemd naar de Britse wiskundige Alan Baker. De stelling van Baker verzamelde vele eerdere resultaten in de transcendentale getaltheorie en loste een probleem op dat bijna vijftien jaar eerder door Aleksander Gelfond was gesteld. Baker gebruikte dit om de transcendentie van veel getallen te bewijzen, om doeltreffende grenzen af te leiden voor de oplossingen van sommige diofantische vergelijkingen en om het probleem op te lossen van het vinden van alle imaginaire kwadratische velden met 1.</span><small> (nl)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink"><small>dbo:</small>wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://www.numdam.org/item%3Fid=SB_1969-1970__12__73_0" href="http://www.numdam.org/item%3Fid=SB_1969-1970__12__73_0">http://www.numdam.org/item%3Fid=SB_1969-1970__12__73_0</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://books.google.com/books%3Fisbn=0486495264" href="https://books.google.com/books%3Fisbn=0486495264">https://books.google.com/books%3Fisbn=0486495264</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://books.google.com/books%3Fisbn=3-540-66785-7" href="https://books.google.com/books%3Fisbn=3-540-66785-7">https://books.google.com/books%3Fisbn=3-540-66785-7</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://books.google.com/books%3Fisbn=052139791X" href="https://books.google.com/books%3Fisbn=052139791X">https://books.google.com/books%3Fisbn=052139791X</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://books.google.com/books%3Fisbn=978-0-521-88268-2" href="https://books.google.com/books%3Fisbn=978-0-521-88268-2">https://books.google.com/books%3Fisbn=978-0-521-88268-2</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID"><small>dbo:</small>wikiPageID</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageID" datatype="xsd:integer" >28751817</span><small> (xsd:integer)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageLength"><small>dbo:</small>wikiPageLength</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageLength" datatype="xsd:nonNegativeInteger" >20915</span><small> (xsd:nonNegativeInteger)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageRevisionID"><small>dbo:</small>wikiPageRevisionID</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageRevisionID" datatype="xsd:integer" >1122130056</span><small> (xsd:integer)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageWikiLink"><small>dbo:</small>wikiPageWikiLink</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Cambridge_University_Press" href="http://dbpedia.org/resource/Cambridge_University_Press"><small>dbr</small>:Cambridge_University_Press</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Quadratic_field" href="http://dbpedia.org/resource/Quadratic_field"><small>dbr</small>:Quadratic_field</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/P-adic_exponential_function" href="http://dbpedia.org/resource/P-adic_exponential_function"><small>dbr</small>:P-adic_exponential_function</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Algebraic_independence" href="http://dbpedia.org/resource/Algebraic_independence"><small>dbr</small>:Algebraic_independence</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Schanuel's_conjecture" href="http://dbpedia.org/resource/Schanuel's_conjecture"><small>dbr</small>:Schanuel's_conjecture</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category:Theorems_in_number_theory" href="http://dbpedia.org/resource/Category:Theorems_in_number_theory"><small>dbc</small>:Theorems_in_number_theory</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Complex_number" href="http://dbpedia.org/resource/Complex_number"><small>dbr</small>:Complex_number</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Analytic_subgroup_theorem" href="http://dbpedia.org/resource/Analytic_subgroup_theorem"><small>dbr</small>:Analytic_subgroup_theorem</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category:Transcendental_numbers" href="http://dbpedia.org/resource/Category:Transcendental_numbers"><small>dbc</small>:Transcendental_numbers</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Gelfond–Schneider_theorem" href="http://dbpedia.org/resource/Gelfond–Schneider_theorem"><small>dbr</small>:Gelfond–Schneider_theorem</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Siegel's_lemma" href="http://dbpedia.org/resource/Siegel's_lemma"><small>dbr</small>:Siegel's_lemma</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Crelle's_Journal" href="http://dbpedia.org/resource/Crelle's_Journal"><small>dbr</small>:Crelle's_Journal</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Logarithm" href="http://dbpedia.org/resource/Logarithm"><small>dbr</small>:Logarithm</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Six_exponentials_theorem" href="http://dbpedia.org/resource/Six_exponentials_theorem"><small>dbr</small>:Six_exponentials_theorem</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Leopoldt's_conjecture" href="http://dbpedia.org/resource/Leopoldt's_conjecture"><small>dbr</small>:Leopoldt's_conjecture</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Mathematika" href="http://dbpedia.org/resource/Mathematika"><small>dbr</small>:Mathematika</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Gisbert_Wüstholz" href="http://dbpedia.org/resource/Gisbert_Wüstholz"><small>dbr</small>:Gisbert_Wüstholz</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Alexander_Gelfond" href="http://dbpedia.org/resource/Alexander_Gelfond"><small>dbr</small>:Alexander_Gelfond</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Algebraic_number" href="http://dbpedia.org/resource/Algebraic_number"><small>dbr</small>:Algebraic_number</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Algebraic_number_theory" href="http://dbpedia.org/resource/Algebraic_number_theory"><small>dbr</small>:Algebraic_number_theory</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Fields_medal" href="http://dbpedia.org/resource/Fields_medal"><small>dbr</small>:Fields_medal</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Number_field" href="http://dbpedia.org/resource/Number_field"><small>dbr</small>:Number_field</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Four_exponentials_conjecture" href="http://dbpedia.org/resource/Four_exponentials_conjecture"><small>dbr</small>:Four_exponentials_conjecture</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Height_function" href="http://dbpedia.org/resource/Height_function"><small>dbr</small>:Height_function</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Academic_Press" href="http://dbpedia.org/resource/Academic_Press"><small>dbr</small>:Academic_Press</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Effective_results_in_number_theory" href="http://dbpedia.org/resource/Effective_results_in_number_theory"><small>dbr</small>:Effective_results_in_number_theory</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Homogeneous_polynomial" href="http://dbpedia.org/resource/Homogeneous_polynomial"><small>dbr</small>:Homogeneous_polynomial</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Diophantine_equations" href="http://dbpedia.org/resource/Diophantine_equations"><small>dbr</small>:Diophantine_equations</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Dover_Publications" href="http://dbpedia.org/resource/Dover_Publications"><small>dbr</small>:Dover_Publications</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Auxiliary_function" href="http://dbpedia.org/resource/Auxiliary_function"><small>dbr</small>:Auxiliary_function</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Class_number_problem" href="http://dbpedia.org/resource/Class_number_problem"><small>dbr</small>:Class_number_problem</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Rational_number" href="http://dbpedia.org/resource/Rational_number"><small>dbr</small>:Rational_number</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Vandermonde_matrix" href="http://dbpedia.org/resource/Vandermonde_matrix"><small>dbr</small>:Vandermonde_matrix</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Theodor_Schneider" href="http://dbpedia.org/resource/Theodor_Schneider"><small>dbr</small>:Theodor_Schneider</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Transcendental_number_theory" href="http://dbpedia.org/resource/Transcendental_number_theory"><small>dbr</small>:Transcendental_number_theory</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Vandermonde_determinant" href="http://dbpedia.org/resource/Vandermonde_determinant"><small>dbr</small>:Vandermonde_determinant</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Springer-Verlag" href="http://dbpedia.org/resource/Springer-Verlag"><small>dbr</small>:Springer-Verlag</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/P-adic" href="http://dbpedia.org/resource/P-adic"><small>dbr</small>:P-adic</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Class_numbers_of_imaginary_quadratic_fields" href="http://dbpedia.org/resource/Class_numbers_of_imaginary_quadratic_fields"><small>dbr</small>:Class_numbers_of_imaginary_quadratic_fields</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Hermite–Lindemann_theorem" href="http://dbpedia.org/resource/Hermite–Lindemann_theorem"><small>dbr</small>:Hermite–Lindemann_theorem</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/authorlink"><small>dbp:</small>authorlink</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:authorlink" lang="en" >Alan Baker</span><small> (en)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/first"><small>dbp:</small>first</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:first" lang="en" >Alan</span><small> (en)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/last"><small>dbp:</small>last</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:last" lang="en" >Baker</span><small> (en)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/mathStatement"><small>dbp:</small>mathStatement</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:mathStatement" lang="en" >If are linearly independent over the rational numbers, then for any algebraic numbers not all zero, we have where H is the maximum of the heights of and C is an effectively computable number depending on n, and the maximum d of the degrees of In particular this number is nonzero, so 1 and are linearly independent over the algebraic numbers.</span><small> (en)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/name"><small>dbp:</small>name</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:name" lang="en" >Baker's Theorem</span><small> (en)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/wikiPageUsesTemplate"><small>dbp:</small>wikiPageUsesTemplate</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Citation" href="http://dbpedia.org/resource/Template:Citation"><small>dbt</small>:Citation</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Harvtxt" href="http://dbpedia.org/resource/Template:Harvtxt"><small>dbt</small>:Harvtxt</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Quotation" href="http://dbpedia.org/resource/Template:Quotation"><small>dbt</small>:Quotation</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Reflist" href="http://dbpedia.org/resource/Template:Reflist"><small>dbt</small>:Reflist</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Short_description" href="http://dbpedia.org/resource/Template:Short_description"><small>dbt</small>:Short_description</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Harvs" href="http://dbpedia.org/resource/Template:Harvs"><small>dbt</small>:Harvs</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Math_theorem" href="http://dbpedia.org/resource/Template:Math_theorem"><small>dbt</small>:Math_theorem</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/year"><small>dbp:</small>year</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:year" datatype="xsd:integer" >1966</span><small> (xsd:integer)</small></span></li> <li><span class="literal"><span property="dbp:year" datatype="xsd:integer" >1967</span><small> (xsd:integer)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://purl.org/dc/terms/subject"><small>dcterms:</small>subject</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dcterms:subject" resource="http://dbpedia.org/resource/Category:Theorems_in_number_theory" prefix="dcterms: http://purl.org/dc/terms/" href="http://dbpedia.org/resource/Category:Theorems_in_number_theory"><small>dbc</small>:Theorems_in_number_theory</a></span></li> <li><span class="literal"><a class="uri" rel="dcterms:subject" resource="http://dbpedia.org/resource/Category:Transcendental_numbers" prefix="dcterms: http://purl.org/dc/terms/" href="http://dbpedia.org/resource/Category:Transcendental_numbers"><small>dbc</small>:Transcendental_numbers</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/1999/02/22-rdf-syntax-ns#type"><small>rdf:</small>type</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatMathematicalTheorems" href="http://dbpedia.org/class/yago/WikicatMathematicalTheorems"><small>yago</small>:WikicatMathematicalTheorems</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatTheoremsInAlgebra" href="http://dbpedia.org/class/yago/WikicatTheoremsInAlgebra"><small>yago</small>:WikicatTheoremsInAlgebra</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatTheoremsInComplexAnalysis" href="http://dbpedia.org/class/yago/WikicatTheoremsInComplexAnalysis"><small>yago</small>:WikicatTheoremsInComplexAnalysis</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatTheoremsInNumberTheory" href="http://dbpedia.org/class/yago/WikicatTheoremsInNumberTheory"><small>yago</small>:WikicatTheoremsInNumberTheory</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatTranscendentalNumbers" href="http://dbpedia.org/class/yago/WikicatTranscendentalNumbers"><small>yago</small>:WikicatTranscendentalNumbers</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Abstraction100002137" href="http://dbpedia.org/class/yago/Abstraction100002137"><small>yago</small>:Abstraction100002137</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Communication100033020" href="http://dbpedia.org/class/yago/Communication100033020"><small>yago</small>:Communication100033020</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/ComplexNumber113729428" href="http://dbpedia.org/class/yago/ComplexNumber113729428"><small>yago</small>:ComplexNumber113729428</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/DefiniteQuantity113576101" href="http://dbpedia.org/class/yago/DefiniteQuantity113576101"><small>yago</small>:DefiniteQuantity113576101</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/IrrationalNumber113730584" href="http://dbpedia.org/class/yago/IrrationalNumber113730584"><small>yago</small>:IrrationalNumber113730584</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Measure100033615" href="http://dbpedia.org/class/yago/Measure100033615"><small>yago</small>:Measure100033615</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Message106598915" href="http://dbpedia.org/class/yago/Message106598915"><small>yago</small>:Message106598915</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Number113582013" href="http://dbpedia.org/class/yago/Number113582013"><small>yago</small>:Number113582013</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Proposition106750804" href="http://dbpedia.org/class/yago/Proposition106750804"><small>yago</small>:Proposition106750804</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/RealNumber113729902" href="http://dbpedia.org/class/yago/RealNumber113729902"><small>yago</small>:RealNumber113729902</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Statement106722453" href="http://dbpedia.org/class/yago/Statement106722453"><small>yago</small>:Statement106722453</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Theorem106752293" href="http://dbpedia.org/class/yago/Theorem106752293"><small>yago</small>:Theorem106752293</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/TranscendentalNumber113730756" href="http://dbpedia.org/class/yago/TranscendentalNumber113730756"><small>yago</small>:TranscendentalNumber113730756</a></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment"><small>rdfs:</small>comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ar" >تدخل مبرهنة باكر في إطار نظرية الأعداد المتسامية، ونعطي أدنى حد لقيمة مطلقة من التركيبات الخطية من لوغاريتمات الأعداد الجبرية. سميت هذه المبرهنة هكذا نسبة إلى آلان باكر.</span><small> (ar)</small></span></li> <li><span class="literal"><span property="rdfs:comment" lang="en" >In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. The result, proved by Alan Baker , subsumed many earlier results in transcendental number theory and solved a problem posed by Alexander Gelfond nearly fifteen years earlier.Baker used this to prove the transcendence of many numbers, to derive effective bounds for the solutions of some Diophantine equations, and to solve the class number problem of finding all imaginary quadratic fields with class number 1.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >Le théorème de Baker résout la conjecture de Gelfond. Publié par Alan Baker en 1966 et 1967, c'est un résultat de transcendance sur les logarithmes de nombres algébriques, qui généralise à la fois le théorème d'Hermite-Lindemann (1882) et le théorème de Gelfond-Schneider (1934). Ce théorème a été adapté au cas des nombres p-adiques par ; le permet de démontrer la conjecture de Leopoldt dans le cas d'un corps de nombres abélien, suivant un article d'Ax.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ja" >ベイカーの定理（ベイカーのていり、英: Baker's theorem）とは、1966年-1968年にかけて、アラン・ベイカーによって発表された、対数関数の一次形式に対する線形独立性、および下界の評価に関する一連の定理のことである。下界の評価が計算可能であることから、数論の様々な分野で応用されている。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="nl" >In de transcendentietheorie, een deelgebied van de wiskunde, geeft de stelling van Baker een ondergrens voor lineaire combinaties van logaritmen van algebraïsche getallen. De stelling is bewezen door en vernoemd naar de Britse wiskundige Alan Baker. De stelling van Baker verzamelde vele eerdere resultaten in de transcendentale getaltheorie en loste een probleem op dat bijna vijftien jaar eerder door Aleksander Gelfond was gesteld. Baker gebruikte dit om de transcendentie van veel getallen te bewijzen, om doeltreffende grenzen af te leiden voor de oplossingen van sommige diofantische vergelijkingen en om het probleem op te lossen van het vinden van alle imaginaire kwadratische velden met 1.</span><small> (nl)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ar" >مبرهنة باكر</span><small> (ar)</small></span></li> <li><span class="literal"><span property="rdfs:label" lang="en" >Baker's theorem</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >Théorème de Baker</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ja" >ベイカーの定理</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="nl" >Stelling van Baker</span><small> (nl)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.0dddsrd" href="http://rdf.freebase.com/ns/m.0dddsrd"><small>freebase</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://yago-knowledge.org/resource/Baker's_theorem" href="http://yago-knowledge.org/resource/Baker's_theorem"><small>yago-res</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://www.wikidata.org/entity/Q3527009" href="http://www.wikidata.org/entity/Q3527009"><small>wikidata</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://ar.dbpedia.org/resource/مبرهنة_باكر" href="http://ar.dbpedia.org/resource/مبرهنة_باكر"><small>dbpedia-ar</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://fa.dbpedia.org/resource/قضیه_بیکر" href="http://fa.dbpedia.org/resource/قضیه_بیکر"><small>dbpedia-fa</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://fr.dbpedia.org/resource/Théorème_de_Baker" href="http://fr.dbpedia.org/resource/Théorème_de_Baker"><small>dbpedia-fr</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://ja.dbpedia.org/resource/ベイカーの定理" href="http://ja.dbpedia.org/resource/ベイカーの定理"><small>dbpedia-ja</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://nl.dbpedia.org/resource/Stelling_van_Baker" href="http://nl.dbpedia.org/resource/Stelling_van_Baker"><small>dbpedia-nl</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://pms.dbpedia.org/resource/Teorema_ëd_Baker" href="http://pms.dbpedia.org/resource/Teorema_ëd_Baker"><small>dbpedia-pms</small>:Baker's theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="https://global.dbpedia.org/id/3FbK4" href="https://global.dbpedia.org/id/3FbK4">https://global.dbpedia.org/id/3FbK4</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/ns/prov#wasDerivedFrom"><small>prov:</small>wasDerivedFrom</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="prov:wasDerivedFrom" resource="http://en.wikipedia.org/wiki/Baker's_theorem?oldid=1122130056&ns=0" href="http://en.wikipedia.org/wiki/Baker's_theorem?oldid=1122130056&ns=0"><small>wikipedia-en</small>:Baker's_theorem?oldid=1122130056&ns=0</a></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://xmlns.com/foaf/0.1/isPrimaryTopicOf"><small>foaf:</small>isPrimaryTopicOf</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="foaf:isPrimaryTopicOf" resource="http://en.wikipedia.org/wiki/Baker's_theorem" href="http://en.wikipedia.org/wiki/Baker's_theorem"><small>wikipedia-en</small>:Baker's_theorem</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2">is <a class="uri" href="http://dbpedia.org/ontology/knownFor"><small>dbo:</small>knownFor</a> of</td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rev="dbo:knownFor" resource="http://dbpedia.org/resource/Alan_Baker_(mathematician)" href="http://dbpedia.org/resource/Alan_Baker_(mathematician)"><small>dbr</small>:Alan_Baker_(mathematician)</a></span></li> </ul></td></tr><tr class="even"><td class="col-2">is <a class="uri" href="http://dbpedia.org/ontology/wikiPageRedirects"><small>dbo:</small>wikiPageRedirects</a> of</td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rev="dbo:wikiPageRedirects" resource="http://dbpedia.org/resource/Linear_forms_in_logarithms" href="http://dbpedia.org/resource/Linear_forms_in_logarithms"><small>dbr</small>:Linear_forms_in_logarithms</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageRedirects" resource="http://dbpedia.org/resource/Linear_form_in_logarithms" href="http://dbpedia.org/resource/Linear_form_in_logarithms"><small>dbr</small>:Linear_form_in_logarithms</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageRedirects" resource="http://dbpedia.org/resource/Baker's_method" href="http://dbpedia.org/resource/Baker's_method"><small>dbr</small>:Baker's_method</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2">is <a class="uri" href="http://dbpedia.org/ontology/wikiPageWikiLink"><small>dbo:</small>wikiPageWikiLink</a> of</td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Determinant" href="http://dbpedia.org/resource/Determinant"><small>dbr</small>:Determinant</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Alfred_van_der_Poorten" href="http://dbpedia.org/resource/Alfred_van_der_Poorten"><small>dbr</small>:Alfred_van_der_Poorten</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Index_of_logarithm_articles" href="http://dbpedia.org/resource/Index_of_logarithm_articles"><small>dbr</small>:Index_of_logarithm_articles</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Schanuel's_conjecture" href="http://dbpedia.org/resource/Schanuel's_conjecture"><small>dbr</small>:Schanuel's_conjecture</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Analytic_subgroup_theorem" href="http://dbpedia.org/resource/Analytic_subgroup_theorem"><small>dbr</small>:Analytic_subgroup_theorem</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Gelfond–Schneider_theorem" href="http://dbpedia.org/resource/Gelfond–Schneider_theorem"><small>dbr</small>:Gelfond–Schneider_theorem</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Lindemann–Weierstrass_theorem" href="http://dbpedia.org/resource/Lindemann–Weierstrass_theorem"><small>dbr</small>:Lindemann–Weierstrass_theorem</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Linear_forms_in_logarithms" href="http://dbpedia.org/resource/Linear_forms_in_logarithms"><small>dbr</small>:Linear_forms_in_logarithms</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Six_exponentials_theorem" href="http://dbpedia.org/resource/Six_exponentials_theorem"><small>dbr</small>:Six_exponentials_theorem</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Leopoldt's_conjecture" href="http://dbpedia.org/resource/Leopoldt's_conjecture"><small>dbr</small>:Leopoldt's_conjecture</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Trigonometric_functions" href="http://dbpedia.org/resource/Trigonometric_functions"><small>dbr</small>:Trigonometric_functions</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Gisbert_Wüstholz" href="http://dbpedia.org/resource/Gisbert_Wüstholz"><small>dbr</small>:Gisbert_Wüstholz</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Alan_Baker_(mathematician)" href="http://dbpedia.org/resource/Alan_Baker_(mathematician)"><small>dbr</small>:Alan_Baker_(mathematician)</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Fields_Medal" href="http://dbpedia.org/resource/Fields_Medal"><small>dbr</small>:Fields_Medal</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Diophantine_approximation" href="http://dbpedia.org/resource/Diophantine_approximation"><small>dbr</small>:Diophantine_approximation</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Four_exponentials_conjecture" href="http://dbpedia.org/resource/Four_exponentials_conjecture"><small>dbr</small>:Four_exponentials_conjecture</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Hilbert's_seventh_problem" href="http://dbpedia.org/resource/Hilbert's_seventh_problem"><small>dbr</small>:Hilbert's_seventh_problem</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Lehmer's_conjecture" href="http://dbpedia.org/resource/Lehmer's_conjecture"><small>dbr</small>:Lehmer's_conjecture</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Height_function" href="http://dbpedia.org/resource/Height_function"><small>dbr</small>:Height_function</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/John_H._Coates" href="http://dbpedia.org/resource/John_H._Coates"><small>dbr</small>:John_H._Coates</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Effective_results_in_number_theory" href="http://dbpedia.org/resource/Effective_results_in_number_theory"><small>dbr</small>:Effective_results_in_number_theory</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Auxiliary_function" href="http://dbpedia.org/resource/Auxiliary_function"><small>dbr</small>:Auxiliary_function</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Class_number_problem" href="http://dbpedia.org/resource/Class_number_problem"><small>dbr</small>:Class_number_problem</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Rational_dependence" href="http://dbpedia.org/resource/Rational_dependence"><small>dbr</small>:Rational_dependence</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Transcendental_number_theory" href="http://dbpedia.org/resource/Transcendental_number_theory"><small>dbr</small>:Transcendental_number_theory</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Linear_form_in_logarithms" href="http://dbpedia.org/resource/Linear_form_in_logarithms"><small>dbr</small>:Linear_form_in_logarithms</a></span></li> <li><span class="literal"><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Baker's_method" href="http://dbpedia.org/resource/Baker's_method"><small>dbr</small>:Baker's_method</a></span></li> </ul></td></tr><tr class="even"><td class="col-2">is <a class="uri" href="http://dbpedia.org/property/knownFor"><small>dbp:</small>knownFor</a> of</td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rev="dbp:knownFor" resource="http://dbpedia.org/resource/Alan_Baker_(mathematician)" href="http://dbpedia.org/resource/Alan_Baker_(mathematician)"><small>dbr</small>:Alan_Baker_(mathematician)</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2">is <a class="uri" href="http://xmlns.com/foaf/0.1/primaryTopic"><small>foaf:</small>primaryTopic</a> of</td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rev="foaf:primaryTopic" resource="http://en.wikipedia.org/wiki/Baker's_theorem" href="http://en.wikipedia.org/wiki/Baker's_theorem"><small>wikipedia-en</small>:Baker's_theorem</a></span></li> </ul></td></tr> </tbody> </table> </div> </div> </div> </section> <!-- property-table --> <!-- footer --> <section> <div class="container-xl"> <div class="text-center p-4 bg-light"> <a href="https://virtuoso.openlinksw.com/" title="OpenLink Virtuoso"><img class="powered_by" src="/statics/images/virt_power_no_border.png" alt="Powered by OpenLink Virtuoso"/></a>    <a href="http://linkeddata.org/"><img alt="This material is Open Knowledge" src="/statics/images/LoDLogo.gif"/></a>     <a href="http://dbpedia.org/sparql"><img alt="W3C Semantic Web Technology" src="/statics/images/sw-sparql-blue.png"/></a>     <a href="https://opendefinition.org/"><img alt="This material is Open Knowledge" src="/statics/images/od_80x15_red_green.png"/></a>    <span style="display:none;" about="" resource="http://www.w3.org/TR/rdfa-syntax" rel="dc:conformsTo"> <a href="https://validator.w3.org/check?uri=referer"> <img src="https://www.w3.org/Icons/valid-xhtml-rdfa" alt="Valid XHTML + RDFa" /> </a> </span> <br /> <small class="text-muted"> This content was extracted from <a href="http://en.wikipedia.org/wiki/Baker's_theorem">Wikipedia</a> and is licensed under the <a href="http://creativecommons.org/licenses/by-sa/3.0/">Creative Commons Attribution-ShareAlike 3.0 Unported License</a> </small> </div> </div> </section> <!-- #footer --> <!-- scripts --> <script src="https://cdnjs.cloudflare.com/ajax/libs/bootstrap/5.2.1/js/bootstrap.bundle.min.js" integrity="sha512-1TK4hjCY5+E9H3r5+05bEGbKGyK506WaDPfPe1s/ihwRjr6OtL43zJLzOFQ+/zciONEd+sp7LwrfOCnyukPSsg==" crossorigin="anonymous"> </script> </body> </html>