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.
"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."@en
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