扭曲伴随L-值、二面体同余素数和Bloch–Kato猜想

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2020-10-29 DOI:10.1007/s12188-020-00224-w

Neil Dummigan

{"title":"扭曲伴随L-值、二面体同余素数和Bloch–Kato猜想","authors":"Neil Dummigan","doi":"10.1007/s12188-020-00224-w","DOIUrl":null,"url":null,"abstract":"<div>We show that a dihedral congruence prime for a normalised Hecke eigenform f in \\(S_k(\\Gamma _0(D),\\chi _D)\\), where \\(\\chi _D\\) is a real quadratic character, appears in the denominator of the Bloch–Kato conjectural formula for the value at 1 of the twisted adjoint L-function of f. We then use a formula of Zagier to prove that it appears in the denominator of a suitably normalised \\(L(1,{\\mathrm {ad}}^0(g)\\otimes \\chi _D)\\) for some \\(g\\in S_k(\\Gamma _0(D),\\chi _D)\\).</div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"90 2","pages":"215 - 227"},"PeriodicalIF":0.4000,"publicationDate":"2020-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-020-00224-w","citationCount":"2","resultStr":"{\"title\":\"Twisted adjoint L-values, dihedral congruence primes and the Bloch–Kato conjecture\",\"authors\":\"Neil Dummigan\",\"doi\":\"10.1007/s12188-020-00224-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We show that a dihedral congruence prime for a normalised Hecke eigenform f in \\\\(S_k(\\\\Gamma _0(D),\\\\chi _D)\\\\), where \\\\(\\\\chi _D\\\\) is a real quadratic character, appears in the denominator of the Bloch–Kato conjectural formula for the value at 1 of the twisted adjoint L-function of f. We then use a formula of Zagier to prove that it appears in the denominator of a suitably normalised \\\\(L(1,{\\\\mathrm {ad}}^0(g)\\\\otimes \\\\chi _D)\\\\) for some \\\\(g\\\\in S_k(\\\\Gamma _0(D),\\\\chi _D)\\\\).</div>\",\"PeriodicalId\":50932,\"journal\":{\"name\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"volume\":\"90 2\",\"pages\":\"215 - 227\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-10-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s12188-020-00224-w\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12188-020-00224-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-020-00224-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

我们证明了正规化Hecke本征型f在\（S_k（\Gamma_0（D），\chi_D）\）中的二面体同余素数，其中\（\chi_D\）是实二次特征，出现在f的扭曲伴随L函数的1处值的Bloch–Kato猜想公式的分母中。然后，我们使用Zagier的公式来证明它出现在S_k（\Gamma_0（D），\chi _D）中的一些\（g\）的适当归一化的\（L（1，｛\mathrm｛ad｝｝^0（g）\otimes\chi _D）\）的分母中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Twisted adjoint L-values, dihedral congruence primes and the Bloch–Kato conjecture

We show that a dihedral congruence prime for a normalised Hecke eigenform f in \(S_k(\Gamma _0(D),\chi _D)\), where \(\chi _D\) is a real quadratic character, appears in the denominator of the Bloch–Kato conjectural formula for the value at 1 of the twisted adjoint L-function of f. We then use a formula of Zagier to prove that it appears in the denominator of a suitably normalised \(L(1,{\mathrm {ad}}^0(g)\otimes \chi _D)\) for some \(g\in S_k(\Gamma _0(D),\chi _D)\).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.