Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$

Abstract:

In this paper we study the distribution of very short sequences of inversive congruential pseudorandom numbers modulo $2^t$. We derive a new bound on exponential sums with such sequences and use it to estimate their discrepancy. The technique we use is based on the method of N. M. Korobov (1972) of estimating double Weyl sums and a fully explicit form of the Vinogradov mean value theorem due to K. Ford (2002), which has never been used in this area and is very likely to find further applications.