Secondary terms in the asymptotics of moments of L-functions

Adrian Diaconu, Henry Twiss

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1 Scopus citations

Abstract

We propose a refined version of the existing conjectural asymptotic formula for the moments of the family of quadratic Dirichlet L-functions over rational function fields. Our prediction is motivated by two natural conjectures that provide sufficient information to determine the analytic properties (meromorphic continuation, location of poles, and the residue at each pole) of a certain generating function of moments of quadratic L-functions. The number field analogue of our asymptotic formula can be obtained by a similar procedure, the only difference being the contributions coming from the archimedean and even places, which require a separate analysis. To avoid this additional technical issue, we present, for simplicity, the asymptotic formula only in the rational function field setting. This has also the advantage of being much easier to test.

Original languageEnglish (US)
Pages (from-to)243-297
Number of pages55
JournalJournal of Number Theory
Volume252
DOIs
StatePublished - Nov 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

  • Kac-Moody Lie algebras
  • L-functions
  • Moments
  • Root systems
  • Weyl group multiple Dirichlet series

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