Character analogues of the poisson and Euler-MacLaurin summation formulas with applications

Research output: Contribution to journalArticle

Abstract

Character versions of the Poisson and Euler-Maclaurin summation formulas are derived. Instead of Bernoulli numbers and polynomials which appear in the classical Euler-Maclaurin formula, generalized Bernoulli numbers and polynomials now appear. Many applications of the results are given. In particular, applications are made to the evaluation of L-functions, the derivation of a character analogue of the Lipschitz summation formula, and the examination of a new character version of the classical gamma function.

Original languageEnglish (US)
Pages (from-to)413-445
Number of pages33
JournalJournal of Number Theory
Volume7
Issue number4
DOIs
StatePublished - Nov 1975

ASJC Scopus subject areas

  • Algebra and Number Theory

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