Nonvanishing of L-function of some Hecke characters on cyclotomic fields

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-07-17 DOI:10.1016/j.jnt.2024.06.002

引用次数: 0

Abstract

In this paper, we show the nonvanishing of some Hecke characters on cyclotomic fields. The main ingredient of this paper is a computation of eigenfunctions and the action of Weil representation at some primes including the primes above 2. As an application, we show that for each isogeny factor of the Jacobian of the p-th Fermat curve where 2 is a quadratic residue modulo p, there are infinitely many twists whose analytic rank is zero. Also, for a certain hyperelliptic curve over the 11-th cyclotomic field whose Jacobian has complex multiplication, there are infinitely many twists whose analytic rank is zero.

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旋积场上某些赫克字符的 L 函数非消失

在这篇论文中，我们展示了循环域上一些赫克特征的非消失性。本文的主要内容是计算一些素数（包括 2 以上的素数）的特征函数和 Weil 表示的作用。作为应用，我们证明了对于第-次费马曲线的雅各布因子的每个等元因子，其中 2 是二次残差模，有无穷多个捻的解析秩为零。另外，对于第 11 个旋回域上的某条超椭圆曲线，其雅各布因子具有复乘法，则有无穷多个阶数为零的捻。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

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.