半积分权值的尖形上的L−函数的零点数

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-05-09 DOI:10.1016/j.jnt.2025.02.014

Pedro Ribeiro

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引用次数: 0

摘要

Meher等人（2019）[21]最近建立了附属于半积分权的某些尖点形式的L -函数在临界线上具有无限多个零。Kim(2023)[18]对附加在由加性字符e(pqn)， pq∈Q扭曲的尖形上的L -函数得到了类似的结果。我们推广了这些作者的结果，给出了这样的零的个数的下界。我们从de la vallsame Poussin方法的一种变体开始，它似乎很有趣，因为它避免了指数和的计算。我们通过使用Lekkerkerker的Hardy-Littlewood方法的变体来改进我们的第一次估计，从而完成了本文。

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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On the number of zeros of L−functions attached to cusp forms of half-integral weight

Meher et al. (2019) [21] have recently established that L−functions attached to certain cusp forms of half-integral weight have infinitely many zeros on the critical line. Kim (2023) [18] obtained analogous results for L−functions attached to cusp forms twisted by an additive character

e (\frac{p}{q} n)

\frac{p}{q} \in Q

. We extend the results of these authors by giving a lower bound for the number of such zeros.

We start by developing a variant of a method of de la Vallée Poussin which seems to have interest as it avoids the evaluation of exponential sums. We finish the paper with an improvement of our first estimate by using Lekkerkerker's variant of the Hardy-Littlewood method.

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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.