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

Bruce C. Berndt

Research output: Contribution to journalArticlepeer-review


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
StatePublished - Apr 1973


  • 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

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Generalized dedekind eta-functions and generalized dedekind sums(i)'. Together they form a unique fingerprint.

Cite this