有限域上高属曲线的多重zeta值不求和

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-05-17 DOI:10.1016/j.jnt.2024.04.014

Daichi Matsuzuki

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引用次数: 0

摘要

在本文中，我们证明了在与给定曲线上有理点∞相关的间隙序列的特定假设下，与有限域上高属代数曲线的函数域相关的∞-adic多重zeta值不为零。利用 Sheats 和 Thakur 对投影线的论证和结果，我们计算了定义多重zeta 值的数列中的幂和的绝对值，并证明该计算暗示了不相等的结果。

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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Non-vanishing of multiple zeta values for higher genus curves over finite fields

In this paper, we show that ∞-adic multiple zeta values associated to the function field of an algebraic curve of higher genus over a finite field are not zero, under certain assumption on the gap sequence associated to the rational point ∞ on the given curve. Using arguments and results of Sheats and Thakur for the case of the projective line, we calculate the absolute values of power sums in the series defining multiple zeta values, and show that the calculation implies the non-vanishing result.

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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.