TY - JOUR
T1 - Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers
AU - El-Mahassni, Edwin D.
AU - Shparlinski, Igor E.
AU - Winterhof, Arne
PY - 2006/8
Y1 - 2006/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33746405179&partnerID=8YFLogxK
U2 - 10.1007/s00605-005-0355-7
DO - 10.1007/s00605-005-0355-7
M3 - Article
AN - SCOPUS:33746405179
SN - 0026-9255
VL - 148
SP - 297
EP - 307
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 4
ER -