Upper bounds for L-functions in positive characteristic

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-06-13 DOI:10.1016/j.ffa.2025.102677

Si-Han Liu , Jia-Yan Yao

引用次数: 0

Abstract

Let

F_{q}

be the finite field with q elements, and K an algebraic function field over

F_{q}

with

F_{q}

as its field of constants. In this work we shall establish the upper bounds for the zeta function

ζ_{K} (s)

and the L-function

L_{K} (s, χ)

with

0 < Re (s) < 1

, where χ is a Hecke character over K. In particular, for

Re (s) = 1 / 2

, we obtain an upper bound of the Lindelöf's type.

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l -函数正特征的上界

设Fq是有q个元素的有限域，K是Fq上的一个代数函数域，Fq是它的常数域。在这项工作中，我们将建立ζ函数ζK(s)和l函数LK（s,χ）的上界，其中0<；Re(s)<1，其中χ是k上的赫克字符。特别地，对于Re(s)=1/2，我们得到了Lindelöf类型的上界。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.