{"title":"黑塞三次曲线和超几何函数的调节器","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":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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
摘要
我们在黑塞立方曲线的动机同调中构建了一些积分元素，并用广义超几何函数和坎佩-德-费里埃特超几何函数来表达它们的调节器。通过使用这些超几何表达式，我们获得了布洛赫-贝林森猜想在 L 函数特殊值上的数值示例。
Regulator of the Hesse cubic curves and hypergeometric functions
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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