实数二次域的分环zp扩展上椭圆曲线的模性

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-06-05 DOI:10.1016/j.jnt.2025.04.018

Sho Yoshikawa

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引用次数: 0

摘要

在假定扭曲l函数中心值的代数部分为p进单位的条件下，证明了在实二次域的环形zp扩展上定义的所有椭圆曲线是模的。我们的结果是X. Zhang的一个结果的细化，它是Thorne的一个结果的实二次模拟。

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Modularity of elliptic curves over cyclotomic Zp-extensions of real quadratic fields

We prove that all elliptic curves defined over the cyclotomic

Z_{p}

-extension of a real quadratic field are modular under the assumption that the algebraic part of the central value of a twisted L-function is a p-adic unit. Our result is a refinement of a result of X. Zhang, which is a real quadratic analogue of a result of Thorne.

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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.