{"title":"Regulator of the Hesse cubic curves and hypergeometric functions","authors":"Yusuke Nemoto","doi":"10.1007/s00229-024-01587-7","DOIUrl":null,"url":null,"abstract":"<p>We construct some integral elements in the motivic cohomology of the Hesse cubic curves and express their regulators in terms of generalized hypergeometric functions and Kampé de Fériet hypergeometric functions. By using these hypergeometric expressions, we obtain numerical examples of the Bloch-Beilinson conjecture on special values of <i>L</i>-functions.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"143 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Manuscripta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01587-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct some integral elements in the motivic cohomology of the Hesse cubic curves and express their regulators in terms of generalized hypergeometric functions and Kampé de Fériet hypergeometric functions. By using these hypergeometric expressions, we obtain numerical examples of the Bloch-Beilinson conjecture on special values of L-functions.
期刊介绍：
manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.
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