Nonvanishing of hyperelliptic zeta functions over finite fields

Jordan S. Ellenberg; Wanlin Li; Mark Shusterman

doi:10.2140/ant.2020.14.1895

Nonvanishing of hyperelliptic zeta functions over finite fields

Jordan S. Ellenberg, Wanlin Li, Mark Shusterman

Research output: Contribution to journal › Article › peer-review

Abstract

Fixing t ϵ 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.

Original language	English
Pages (from-to)	1895-1909
Number of pages	15
Journal	Algebra and Number Theory
Volume	14
Issue number	7
DOIs	https://doi.org/10.2140/ant.2020.14.1895
State	Published - 2020
Externally published	Yes

Keywords

Dirichlet characters
Function fields
L-functions
Nonvanishing

Access to Document

10.2140/ant.2020.14.1895

Cite this

@article{4a36f688872042bca9e8f7ccd9570b71,

title = "Nonvanishing of hyperelliptic zeta functions over finite fields",

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

keywords = "Dirichlet characters, Function fields, L-functions, Nonvanishing",

author = "Ellenberg, {Jordan S.} and Wanlin Li and Mark Shusterman",

year = "2020",

doi = "10.2140/ant.2020.14.1895",

language = "אנגלית",

volume = "14",

pages = "1895--1909",

journal = "Algebra and Number Theory",

issn = "1937-0652",

publisher = "Mathematical Sciences Publishers",

number = "7",

}

TY - JOUR

T1 - Nonvanishing of hyperelliptic zeta functions over finite fields

AU - Ellenberg, Jordan S.

AU - Li, Wanlin

AU - Shusterman, Mark

PY - 2020

Y1 - 2020

N2 - Fixing t ϵ R and a finite field Fq of odd characteristic, we give an explicit upper bound on the proportion of genus g hyperelliptic curves over Fq whose zeta function vanishes at 1/2+ it. Our upper bound is independent of g and tends to 0 as q grows.

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

KW - Dirichlet characters

KW - Function fields

KW - L-functions

KW - Nonvanishing

UR - http://www.scopus.com/inward/record.url?scp=85090610498&partnerID=8YFLogxK

U2 - 10.2140/ant.2020.14.1895

DO - 10.2140/ant.2020.14.1895

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85090610498

SN - 1937-0652

VL - 14

SP - 1895

EP - 1909

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 7

ER -

Nonvanishing of hyperelliptic zeta functions over finite fields

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this