Nonvanishing of hyperelliptic zeta functions over finite fields

被引：5

作者：

Ellenberg, Jordan S. ^{[1
]}

Li, Wanlin ^{[2
]}

Shusterman, Mark ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

ALGEBRA & NUMBER THEORY | 2020年 / 14卷 / 07期

关键词：

nonvanishing; L-functions; function fields; Dirichlet characters; DIRICHLET L-FUNCTIONS; ZEROS;

D O I：

10.2140/ant.2020.14.1895

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fixing t is an element of R and a finite field F-q of odd characteristic, we give an explicit upper bound on the proportion of genus g hyperelliptic curves over F-q whose zeta function vanishes at 1/2 + it. Our upper bound is independent of g and tends to 0 as q grows.

引用

页码：1895 / 1909

页数：15

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