Conjectures for the integral moments and ratios of L-functions over function fields

J. C. Andrade*, J. P. Keating

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

26 Citations (Scopus)

Abstract

We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of L-functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of L-functions associated with hyperelliptic curves of genus g over a fixed finite field Fq in the limit as g→ ∞ Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these L-functions.

Original languageEnglish
Pages (from-to)102-148
Number of pages47
JournalJournal of Number Theory
Volume142
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Finite fields
  • Function fields
  • Hyperelliptic curves
  • Moments of quadratic Dirichlet L-functions
  • Primary
  • Random matrix theory
  • Ratios of L-functions
  • Secondary

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