Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers

Edwin D. El-Mahassni*, Igor E. Shparlinski, Arne Winterhof

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present a new bound on the s-dimensional discrepancy of nonlinear congruential pseudorandom numbers over the residue ring ℤM modulo M for an "almost squarefree" integer M. It is useful to recall that almost all integers are of this type. Moreover, if the generator is associated with a permutation polynomial over ℤM we obtain a stronger bound "on average" over all initial values. This bound is new even in the case when M = p is prime.

Original languageEnglish
Pages (from-to)297-307
Number of pages11
JournalMonatshefte fur Mathematik
Volume148
Issue number4
DOIs
Publication statusPublished - Aug 2006

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