ON THE DISCREPANCY OF INVERSIVE CONGRUENTIAL PSEUDORANDOM NUMBERS WITH PRIME POWER MODULUS, II

One of the alternatives to linear congruential pseudorandom number gen erators with their known deficiencies is the inversive congruential me thod with prime power modulus. Recently, it was proved that pairs of i nversive congruential pseudorandom numbers have nice statistical indep endence properties. In the present paper it is shown that a similar re sult cannot be obtained for k-tuples with k greater-than-or-equal-to 3 since their discrepancy is too large. The method of proof relies on t he evaluation of certain exponential sums. In view of the present resu lt the inversive congruential method with prime power modulus seems to be not absolutely suitable for generating uniform pseudorandom number s.