An exact determination of serial correlations of pseudo-random numbers

Ulrich Dieter, Joachim Ahrens

Research output: Contribution to journalArticlepeer-review


Exact expressions for serial correlations of sequences of pseudo-random numbers are derived. The reduction to generalized Dedekind sums is of optimum simplicity and covers all cases of the linear congruential method. The subsequent evaluation of the generalized Dedekind sums is based on a modified Euclidean algorithm whose quotients are recognized as the main contributors to the size of the serial correlations. This leads to the establishment of bounds as well as of fast computer programs. Moreover, some light is thrown upon the general question of quality in random number generation.
Original languageEnglish
Pages (from-to)101-123
JournalNumerische Mathematik
Publication statusPublished - 1971
Externally publishedYes

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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