Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$
Number Theory
2019-06-13 v2
Abstract
In this paper we study the distribution of very short sequences of inversive congruential pseudorandom numbers modulo . We derive a new bound on exponential sums with such sequences and use it to give estimate their discrepancy. The technique we use, based 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), has never been used in this area and is very likely to find further applications.
Keywords
Cite
@article{arxiv.1812.08837,
title = {Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$},
author = {László Mérai and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1812.08837},
year = {2019}
}