Average values of L-functions in characteristic two

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Abstract

Gauss made two conjectures about average values of class numbers of orders in quadratic number fields, later on proven by Lipschitz and Siegel. A version for function fields of odd characteristic was established by Hoffstein and Rosen. In this paper, we extend their results to the case of even characteristic. More precisely, we obtain formulas of average values of L-functions associated to orders in quadratic function fields over a constant field of characteristic two, and then derive formulas of average class numbers of these orders.

Original languageEnglish
Pages (from-to)2138-2158
Number of pages21
JournalJournal of Number Theory
Volume128
Issue number7
DOIs
StatePublished - Jul 2008

Keywords

  • Class numbers
  • L-functions
  • Orders
  • Quadratic function fields

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