An application of the mellin-barnes type of integral to the mean square of l-functions

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Abstract

The mean square of all Dirichlet L-functions (mod q), in the form (2.1) given below, will be investigated. We establish full asymptotic expansions for (2.1) (see Theorems 1 and 2) by introducing the Mellin-Bames type of integral formula (3.4) for the infinite double sum (3.2). Our treatment of (2.1) becomes, by virtue of (3.4), considerably simpler than the existing methods. Further improvements (Theorems A and B) are also given.

Original languageEnglish
Pages (from-to)77-88
Number of pages12
JournalLithuanian Mathematical Journal
Volume38
Issue number1
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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