Dedekind sums and class numbers

Bruce C. Berndt, Ronald J. Evans

Research output: Contribution to journalArticle

Abstract

Formulas for the class number of an imaginary quadratic number field are proved. Some of these formulas were previously established by Berndt and by Goldstein and Razar with the use of analytic methods. The proofs given here use Dirichlet's classical class number formula, but otherwise the proofs are completely elementary. A key ingredient in the proofs is the reciprocity theorem for Dedekind-Rademacher sums.

Original languageEnglish (US)
Pages (from-to)265-273
Number of pages9
JournalMonatshefte für Mathematik
Volume84
Issue number4
DOIs
StatePublished - Dec 1 1977

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Dedekind Sums
Class number
Quadratic field
Reciprocity
Number field
Dirichlet
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Dedekind sums and class numbers. / Berndt, Bruce C.; Evans, Ronald J.

In: Monatshefte für Mathematik, Vol. 84, No. 4, 01.12.1977, p. 265-273.

Research output: Contribution to journalArticle

Berndt, Bruce C. ; Evans, Ronald J. / Dedekind sums and class numbers. In: Monatshefte für Mathematik. 1977 ; Vol. 84, No. 4. pp. 265-273.
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