Moments of quadratic dirichlet L-functions over rational function fields

Alina Bucur, Adrian Diaconu

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15 Scopus citations

Abstract

We establish the meromorphic continuation of a multiple Dirichlet series associated to the fourth moment of quadratic Dirichlet L-functions, over the rational function field Fq(T) with q odd, up to its natural boundary. This is the first such result in which the group of functional equations is infinite; in such cases, it is expected that the series cannot be continued everywhere but can at least be extended to a large enough region to deduce asymptotics at the central point. In this case, these asymptotics coincide with existing predictions for the fourth moment of the symplectic family of quadratic Dirichlet L-functions. The construction uses the Weyl group action of a particular Kac-Moody algebra; this suggests an approach to higher moments using appropriate non-affine Kac-Moody algebras.

Original languageEnglish (US)
Pages (from-to)485-517
Number of pages33
JournalMoscow Mathematical Journal
Volume10
Issue number3
DOIs
StatePublished - 2010

Keywords

  • Coxeter group
  • Finite field
  • Moments of quadratic dirichlet l-functions
  • Multiple dirichlet series
  • Rational function field
  • Roots

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