Notes on Generalized Dedekind Sums.

Abstract

Generalized Dedekind sums sigma(h,k,c) have proved to be useful in connection with the analysis of linear congruential random number generators. This paper introduces a simple algorithm for the calculation of generalized Dedekind sums using only integer arithmetic. A second algorithm, for calculating the value of c which maximizes or minimizes sigma(h,k,c) when h and k are given, is used to deduce optimal a priori bounds on sigma(h,k,c). Finally the reciprocity law for Dedekind sums is shown to be a consequence of a much more general reciprocity law.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1975
Accession Number
ADA008804

Entities

People

  • Donald Knuth

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Generators
  • Mathematics
  • Random Number Generators

Fields of Study

  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Theoretical Analysis.