{"title":"论克罗斯特曼连接的扭曲矩周期","authors":"Ping-Hsun Chuang, Jeng-Daw Yu","doi":"10.1007/s11139-024-00936-0","DOIUrl":null,"url":null,"abstract":"<p>This paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these associated period numbers in terms of the Bessel moments. Via the rational structures on Betti homology and de Rham cohomology, we prove the <span>\\(\\mathbb {Q}\\)</span>-linear and quadratic relations among these Bessel moments.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the periods of twisted moments of the Kloosterman connection\",\"authors\":\"Ping-Hsun Chuang, Jeng-Daw Yu\",\"doi\":\"10.1007/s11139-024-00936-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these associated period numbers in terms of the Bessel moments. Via the rational structures on Betti homology and de Rham cohomology, we prove the <span>\\\\(\\\\mathbb {Q}\\\\)</span>-linear and quadratic relations among these Bessel moments.</p>\",\"PeriodicalId\":501430,\"journal\":{\"name\":\"The Ramanujan Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Ramanujan Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11139-024-00936-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00936-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文旨在研究环上二阶 Kloosterman 连接的扭曲对称幂的贝蒂同调与 de Rham 同调。我们计算了周期配对，并根据某些基，用贝塞尔矩解释了这些相关的周期数。通过贝蒂同构和德拉姆同构的合理结构，我们证明了这些贝塞尔矩之间的线性和二次关系。
On the periods of twisted moments of the Kloosterman connection
This paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these associated period numbers in terms of the Bessel moments. Via the rational structures on Betti homology and de Rham cohomology, we prove the \(\mathbb {Q}\)-linear and quadratic relations among these Bessel moments.
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