Document Zbl 0126.06903

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Circ. Mat. Palermo (2)</a> <a href="/?q=in%3A132152" title="Articles in this Issue">7, 185-244 (1958)</a>. </div> <div class="abstract"><div class="reviewer"> Reviewer: <a href="/authors/?q=R%2A+Kochend%C3%B6rffer">R. Kochendörffer (Greifswald)</a></div> <div class="clearfix"></div><div class="scan"> <span> Page: <a class="goto" href="/scans/126/064.gif">−5</a> <a class="goto" href="/scans/126/065.gif">−4</a> <a class="goto" href="/scans/126/066.gif">−3</a> <a class="goto" href="/scans/126/067.gif">−2</a> <a class="goto" href="/scans/126/068.gif">−1</a> <a class="goto" href="/scans/126/069.gif">±0</a> <a class="goto" href="/scans/126/070.gif">+1</a> <a class="goto" href="/scans/126/071.gif">+2</a> <a class="goto" href="/scans/126/072.gif">+3</a> <a class="goto" href="/scans/126/073.gif">+4</a> <a class="goto" href="/scans/126/074.gif">+5</a></span> <a class="scan" href="/scans/126/069.gif">Show Scanned Page</a><br> <img src="/scans/126/069.gif" alt="scan of Zbl 0126.06903" onclick="$(this).siblings('.scan').click();"> </div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A3204774">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A3204774">Cited in <strong>9</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A11R18" title="MSC2020">11R18</a> </td> <td class="space"> Cyclotomic extensions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anumber+fields">number fields</a>; <a href="/?q=ut%3Apower+residue+character">power residue character</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0020.29101">Zbl 0020.29101</a>; <a href="/0055.27102">Zbl 0055.27102</a>; <a href="/0010.33803">Zbl 0010.33803</a>; <a href="/0048.27001">Zbl 0048.27001</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0126.06903" data-ciurl="/ci/03204774" data-biburl="/bibtex/03204774.bib" data-amsurl="/amsrefs/03204774.bib" data-xmlurl="/xml/03204774.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/03204774.pdf" title="Zbl 0126.06903 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/BF02854527" aria-label="DOI for “Der $2^n$-te Potenzcharakter von 2 im Körper der $2^n$-ten Einheitswurzeln”" title="10.1007/BF02854527">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="mathoverflow"> <h3>Online Encyclopedia of Integer Sequences:</h3> <a href="https://oeis.org/A45315">Primes p such that x^8 = 2 has a solution mod p.</a><br> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A. AIGNER,Kriterium zum 8. und 16. Potenzcharakter der Reste 2 und–2.–Deutsche Math.4 (1939), 44–52. · <a href="/65.0112.02" class="nowrap">JFM 65.0112.02</a></td> </tr><tr> <td>[2]</td> <td class="space">E. ARTIN–H. HASSE,Die beiden Ergänzungssätze zum Reziprozitätsgesetz der l n-ten Potenzreste im Körper der ln-ten Einheitswurzeln.–Abh. Math. Sem. Hamburg6 (1928), 146–162. · <a href="/54.0191.05" class="nowrap">JFM 54.0191.05</a> · <a href="https://doi.org/10.1007/BF02940607" class="nowrap">doi:10.1007/BF02940607</a></td> </tr><tr> <td>[3]</td> <td class="space">N. G. W. H. BEEGER,A problem of the theory of numbers and its history.–Nieuw Arch. Wisk. (2)22 (1948), 306–309. · <a href="/0029.25202" class="nowrap">Zbl 0029.25202</a></td> </tr><tr> <td>[4]</td> <td class="space">A. CUNNINGHAM,On 2 as a 16-ic residue.–Proc. London Math. Soc. (1)27 (1895), 85–122. · <a href="/27.0146.02" class="nowrap">JFM 27.0146.02</a> · <a href="https://doi.org/10.1112/plms/s1-27.1.85" class="nowrap">doi:10.1112/plms/s1-27.1.85</a></td> </tr><tr> <td>[5]</td> <td class="space">H. DAVENPORT–H. HASSE,Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen.–Journ. reine angew. Math.172 (1934), 151–182. · <a href="/60.0913.01" class="nowrap">JFM 60.0913.01</a></td> </tr><tr> <td>[6]</td> <td class="space">Y. FURUTA,A reciprocity law of the power residue symbol.–Journ. Math. Soc. Japan10 (1958), 46–54. · <a href="/0083.26002" class="nowrap">Zbl 0083.26002</a> · <a href="https://doi.org/10.2969/jmsj/01010046" class="nowrap">doi:10.2969/jmsj/01010046</a></td> </tr><tr> <td>[7]</td> <td class="space">C. F. GAUSS,Disquisitiones arithmeticae.–Leipzig 1801=Werke1.</td> </tr><tr> <td>[8]</td> <td class="space">C. F. GAUSS,Theoria residuorum biquadraticorum I.–Comm. soc. reg. scient. Gotting. rec.6 (1828) = Werke2, 65–92.</td> </tr><tr> <td>[9]</td> <td class="space">F. GOLDSCHEIDER,Das Reziprozitätsgesetz der 8-ten Potenzreste.–Wiss. Beitr. z. Progr. d. Luisenstädt. Realgymn. Berlin 1899, 29 S.</td> </tr><tr> <td>[10]</td> <td class="space">H. HASSE,Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper II.–Jahresber. Deutsche Math.–Ver., Erg. Bd.6 (1930). · <a href="/56.0165.01" class="nowrap">JFM 56.0165.01</a></td> </tr><tr> <td>[11]</td> <td class="space">H. HASSE,Über die Klassenzahl Abelscher Zahlkörper.–Berlin 1952. · <a href="/0063.01966" class="nowrap">Zbl 0063.01966</a></td> </tr><tr> <td>[12]</td> <td class="space">H. HASSE,Zetafunktion und L-Funktionen zu einem arithmetischen Funktionenkörper vom Fermatschen Typus.–Abh. Deutsche Akad. Wiss. Berlin, Kl. f. Math. u. Naturwiss., Jahrg. 1954, Heft 4 (1955), 68 S.</td> </tr><tr> <td>[13]</td> <td class="space">C. G. REUSCHLE,Mathematische Abhandlung, enthaltend neue zahlentheoretische Tabellen.–Progr. z. Schlusse d. Schuljahres 1855/56 am Kgl. Gymn. z. Stuttgart, 61 S.</td> </tr><tr> <td>[14]</td> <td class="space">L. STICKELBERGER,Über eine Verallgemeinerung der Kreisteilung.–Math. Ann.37 (1890), 321–367. · <a href="/22.0100.01" class="nowrap">JFM 22.0100.01</a> · <a href="https://doi.org/10.1007/BF01721360" class="nowrap">doi:10.1007/BF01721360</a></td> </tr><tr> <td>[15]</td> <td class="space">H. WEBER,Theorie der Abelschen Zahlkörper.–Acta math.8 (1886), 193–263, Abschn. II; siehe auch: Lehrbuch der Algebra2, 2. Aufl., Strassburg 1899, Abschn.24. · <a href="/18.0055.04" class="nowrap">JFM 18.0055.04</a> · <a href="https://doi.org/10.1007/BF02417089" class="nowrap">doi:10.1007/BF02417089</a></td> </tr><tr> <td>[16]</td> <td class="space">A. WEIL,On Jacobi sums as “Grössencharaktere{”.–Trans. Amer. Math. Soc.73 (1952), 487–495.} · <a href="/0048.27001" class="nowrap">Zbl 0048.27001</a></td> </tr><tr> <td>[17]</td> <td class="space">A. E. WESTERN,Some criteria for the residues of eighth and other powers.–Proc. London Math. Soc. (2)9 (1911), 244–272. · <a href="/42.0233.01" class="nowrap">JFM 42.0233.01</a> · <a href="https://doi.org/10.1112/plms/s2-9.1.244" class="nowrap">doi:10.1112/plms/s2-9.1.244</a></td> </tr><tr> <td>[18]</td> <td class="space">A. L. WHITEMAN,The sixteenth power residue character of 2.–Canad. Math. Journ6 (1954), 364–373. · <a href="/0055.27102" class="nowrap">Zbl 0055.27102</a> · <a href="https://doi.org/10.4153/CJM-1954-035-8" class="nowrap">doi:10.4153/CJM-1954-035-8</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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