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)

20 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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