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href="https://unsa-ba.academia.edu/">University of Sarajevo</a>, <a class="u-tcGrayDarker" href="https://unsa-ba.academia.edu/Departments/Department_of_mathematics_Odsjek_za_matematiku_/Documents">Department of mathematics (Odsjek za matematiku)</a>, <span class="u-tcGrayDarker">Faculty Member</span></div></div></div></div><div class="sidebar-cta-container"><button class="ds2-5-button hidden profile-cta-button grow js-profile-follow-button" data-broccoli-component="user-info.follow-button" data-click-track="profile-user-info-follow-button" data-follow-user-fname="Muharem" data-follow-user-id="43632767" data-follow-user-source="profile_button" data-has-google="false"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">add</span>Follow</button><button class="ds2-5-button hidden profile-cta-button grow js-profile-unfollow-button" data-broccoli-component="user-info.unfollow-button" data-click-track="profile-user-info-unfollow-button" 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wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/124046718/On_Effective_Upper_Bound_for_Huber_s_Constant">On Effective Upper Bound for Huber’s Constant</a></div><div class="wp-workCard_item"><span>Results in mathematics</span><span>, Jun 14, 2024</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We determine an effective upper bound for Huber&amp;#39;s constant in the prime geodesic theorem ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We determine an effective upper bound for Huber&amp;#39;s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case of orbifolds on which the length of the shortest prime geodesic does not exceed 4/3. Huber&amp;#39;s constant is relevant for obtaining effective, numerically computable, bounds for various analytic quantities which appear in the Arakelov theory of algebraic curves. The result is illustrated by finding an upper bound for this constant on (2,3,7) triangle group. We also calculate an effective upper bound for Faltings&amp;#39;s delta function on the Klein quartic.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="124046718"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="124046718"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 124046718; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=124046718]").text(description); $(".js-view-count[data-work-id=124046718]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 124046718; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='124046718']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 124046718, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=124046718]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":124046718,"title":"On Effective Upper Bound for Huber’s Constant","translated_title":"","metadata":{"abstract":"We determine an effective upper bound for Huber\u0026amp;#39;s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case of orbifolds on which the length of the shortest prime geodesic does not exceed 4/3. Huber\u0026amp;#39;s constant is relevant for obtaining effective, numerically computable, bounds for various analytic quantities which appear in the Arakelov theory of algebraic curves. The result is illustrated by finding an upper bound for this constant on (2,3,7) triangle group. We also calculate an effective upper bound for Faltings\u0026amp;#39;s delta function on the Klein quartic.","publication_date":{"day":14,"month":6,"year":2024,"errors":{}},"publication_name":"Results in mathematics"},"translated_abstract":"We determine an effective upper bound for Huber\u0026amp;#39;s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case of orbifolds on which the length of the shortest prime geodesic does not exceed 4/3. Huber\u0026amp;#39;s constant is relevant for obtaining effective, numerically computable, bounds for various analytic quantities which appear in the Arakelov theory of algebraic curves. The result is illustrated by finding an upper bound for this constant on (2,3,7) triangle group. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="118313847"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/118313847/Effective_bounds_for_Huber_s_constant_and_Faltings_s_delta_function"><img alt="Research paper thumbnail of Effective bounds for Huber’s constant and Faltings’s delta function" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/118313847/Effective_bounds_for_Huber_s_constant_and_Faltings_s_delta_function">Effective bounds for Huber’s constant and Faltings’s delta function</a></div><div class="wp-workCard_item"><span>Mathematics of Computation</span><span>, Mar 24, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic theorem on cofinite Fuchsian groups of the first kind, we refine the constants therein. The newly obtained effective upper bound for Huber’s constant is in the modular surface case approximately 74000 74000 -times smaller than the previously claimed one. The degree of reduction in the case of an upper bound for Faltings’s delta function ranges from 10 8 10^{8} to 10 16 10^{16} .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="118313847"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="118313847"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 118313847; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=118313847]").text(description); $(".js-view-count[data-work-id=118313847]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 118313847; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='118313847']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 118313847, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=118313847]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":118313847,"title":"Effective bounds for Huber’s constant and Faltings’s delta function","translated_title":"","metadata":{"abstract":"By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic theorem on cofinite Fuchsian groups of the first kind, we refine the constants therein. 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/></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/124046730/On_maximal_operators_on_k_spheres_in_Z_n">On maximal operators on k-spheres in Z^n</a></div><div class="wp-workCard_item"><span>Proceedings of the American Mathematical Society</span><span>, 2006</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b01114047a1725c70a3931b29f589cc2" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":118444390,"asset_id":124046730,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/118444390/download_file?st=MTczMjQ0MTQ4Miw4LjIyMi4yMDguMTQ2&st=MTczMjQ0MTQ4MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa 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wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/124046718/On_Effective_Upper_Bound_for_Huber_s_Constant">On Effective Upper Bound for Huber’s Constant</a></div><div class="wp-workCard_item"><span>Results in mathematics</span><span>, Jun 14, 2024</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We determine an effective upper bound for Huber&amp;#39;s constant in the prime geodesic theorem ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We determine an effective upper bound for Huber&amp;#39;s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case of orbifolds on which the length of the shortest prime geodesic does not exceed 4/3. Huber&amp;#39;s constant is relevant for obtaining effective, numerically computable, bounds for various analytic quantities which appear in the Arakelov theory of algebraic curves. The result is illustrated by finding an upper bound for this constant on (2,3,7) triangle group. We also calculate an effective upper bound for Faltings&amp;#39;s delta function on the Klein quartic.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="124046718"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="124046718"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 124046718; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=124046718]").text(description); $(".js-view-count[data-work-id=124046718]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 124046718; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='124046718']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 124046718, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=124046718]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":124046718,"title":"On Effective Upper Bound for Huber’s Constant","translated_title":"","metadata":{"abstract":"We determine an effective upper bound for Huber\u0026amp;#39;s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case of orbifolds on which the length of the shortest prime geodesic does not exceed 4/3. Huber\u0026amp;#39;s constant is relevant for obtaining effective, numerically computable, bounds for various analytic quantities which appear in the Arakelov theory of algebraic curves. The result is illustrated by finding an upper bound for this constant on (2,3,7) triangle group. We also calculate an effective upper bound for Faltings\u0026amp;#39;s delta function on the Klein quartic.","publication_date":{"day":14,"month":6,"year":2024,"errors":{}},"publication_name":"Results in mathematics"},"translated_abstract":"We determine an effective upper bound for Huber\u0026amp;#39;s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case of orbifolds on which the length of the shortest prime geodesic does not exceed 4/3. Huber\u0026amp;#39;s constant is relevant for obtaining effective, numerically computable, bounds for various analytic quantities which appear in the Arakelov theory of algebraic curves. The result is illustrated by finding an upper bound for this constant on (2,3,7) triangle group. We also calculate an effective upper bound for Faltings\u0026amp;#39;s delta function on the Klein quartic.","internal_url":"https://www.academia.edu/124046718/On_Effective_Upper_Bound_for_Huber_s_Constant","translated_internal_url":"","created_at":"2024-09-20T23:15:24.084-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":43632767,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_Effective_Upper_Bound_for_Huber_s_Constant","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":43632767,"first_name":"Muharem","middle_initials":"","last_name":"Avdispahić","page_name":"Avdispahic","domain_name":"unsa-ba","created_at":"2016-02-21T08:31:05.410-08:00","display_name":"Muharem Avdispahić","url":"https://unsa-ba.academia.edu/Avdispahic"},"attachments":[],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"}],"urls":[{"id":44761884,"url":"https://doi.org/10.1007/s00025-024-02211-6"}]}, dispatcherData: dispatcherData }); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="118313847"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/118313847/Effective_bounds_for_Huber_s_constant_and_Faltings_s_delta_function"><img alt="Research paper thumbnail of Effective bounds for Huber’s constant and Faltings’s delta function" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/118313847/Effective_bounds_for_Huber_s_constant_and_Faltings_s_delta_function">Effective bounds for Huber’s constant and Faltings’s delta function</a></div><div class="wp-workCard_item"><span>Mathematics of Computation</span><span>, Mar 24, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic theorem on cofinite Fuchsian groups of the first kind, we refine the constants therein. The newly obtained effective upper bound for Huber’s constant is in the modular surface case approximately 74000 74000 -times smaller than the previously claimed one. The degree of reduction in the case of an upper bound for Faltings’s delta function ranges from 10 8 10^{8} to 10 16 10^{16} .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="118313847"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="118313847"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 118313847; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=118313847]").text(description); $(".js-view-count[data-work-id=118313847]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 118313847; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='118313847']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 118313847, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=118313847]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":118313847,"title":"Effective bounds for Huber’s constant and Faltings’s delta function","translated_title":"","metadata":{"abstract":"By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic theorem on cofinite Fuchsian groups of the first kind, we refine the constants therein. The newly obtained effective upper bound for Huber’s constant is in the modular surface case approximately 74000 74000 -times smaller than the previously claimed one. The degree of reduction in the case of an upper bound for Faltings’s delta function ranges from 10 8 10^{8} to 10 16 10^{16} .","publisher":"American Mathematical Society","publication_date":{"day":24,"month":3,"year":2021,"errors":{}},"publication_name":"Mathematics of Computation"},"translated_abstract":"By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic theorem on cofinite Fuchsian groups of the first kind, we refine the constants therein. The newly obtained effective upper bound for Huber’s constant is in the modular surface case approximately 74000 74000 -times smaller than the previously claimed one. 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