Resumen de Distribution of Nonlinear Congruential Pseudorandom Numbers Modulo Almost Squarefree Integers

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

• 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.