Distribution of Nonlinear Congruential Pseudorandom Numbers Modulo Almost Squarefree Integers

• Autores: Edwin D. El-Mahassni, Igor E. Shparlinski, Arne Winterhof
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 148, Nº 4, 2006, págs. 297-307
• Idioma: inglés
• DOI: 10.1007/s00605-005-0355-7
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• Resumen

  • 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 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 we obtain a stronger bound ¿on average¿ over all initial values. This bound is new even in the case when M = p is prime.