The mean value of L(12,χ) in the hyperelliptic ensemble

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

*Corresponding author for this work

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

37 Citations (Scopus)


We obtain an asymptotic formula for the first moment of quadratic Dirichlet L-functions over the rational function field at the central point s=12. Specifically, we compute the expected value of L(12,χ) for an ensemble of hyperelliptic curves of genus g over a fixed finite field as g→∞. Our approach relies on the use of the analogue of the approximate functional equation for such L-functions. The results presented here are the function field analogues of those obtained previously by Jutila in the number-field setting and are consistent with recent general conjectures for the moments of L-functions motivated by Random Matrix Theory.

Original languageEnglish
Pages (from-to)2793-2816
Number of pages24
JournalJournal of Number Theory
Issue number12
Publication statusPublished - 1 Dec 2012


  • Finite fields
  • Function fields
  • Hyperelliptic curves
  • Moments of quadratic Dirichlet L-functions
  • Random Matrix Theory


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