具有一定Zp扭转的GL(2)上尖形的l值生成切环Hecke场

IF 0.6 3区 数学 Q3 MATHEMATICS
Jaesung Kwon
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引用次数: 0

摘要

设F是一个数域,F是GL(2)上的代数自同构新形式,p是一个奇素数,它不除F的类数和F的阶数。我们证明了F是由F的某z -扩展的伽罗氏字符φ扭曲的l值决定的,并且,如果F是全实数或CM,则在F上的一些温和假设下,f的Hecke场与分环场Q(φ)的复合是由f的伽罗瓦特征φ扭曲的代数l值生成的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generation of cyclotomic Hecke fields by L-values of cusp forms on GL(2) with certain Zp twist
Let F be a number field, f an algebraic automorphic newform on GL(2) over F, p an odd prime does not divide the class number of F and the level of f. We prove that f is determined by its L-values twisted by Galois characters ϕ of certain Zp-extension of F. Furthermore, if F is totally real or CM, then under some mild assumption on f, the compositum of the Hecke field of f and the cyclotomic field Q(ϕ) is generated by the algebraic L-values of f twisted by Galois characters ϕ of certain Zp-extension of F.
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来源期刊
Journal of Number Theory
Journal of Number Theory 数学-数学
CiteScore
1.30
自引率
14.30%
发文量
122
审稿时长
16 weeks
期刊介绍: The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.
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