Nonvanishing of hyperelliptic zeta functions over finite fields

Jordan S. Ellenberg, Wanlin Li, Mark Shusterman

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1895-1909
Number of pages15
JournalAlgebra and Number Theory
Issue number7
StatePublished - 2020
Externally publishedYes


  • Dirichlet characters
  • Function fields
  • L-functions
  • Nonvanishing


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