Generalized dedekind eta-functions and generalized dedekind sums(i)

Research output: Contribution to journalArticle

Abstract

A transformation formula under modular substitutions is derived for a very large class of generalized Eisenstein series. The result also gives a transformation formula for generalized Dedekind eta-functions. Various types of Dedekind sums arise, and reciprocity laws are established.

Original languageEnglish (US)
Pages (from-to)495-508
Number of pages14
JournalTransactions of the American Mathematical Society
Volume178
DOIs
StatePublished - Apr 1973

Keywords

  • Bernoulli numbers and polynomials
  • Dedekind eta-function
  • Dedekind sum
  • Eisenstein series
  • Generalized Dedekind eta-function
  • Generalized Dedekind sum
  • Lambert series
  • Modular transformation
  • Reciprocity law

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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