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.
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页码：1895 / 1909
页数：15
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