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

## TL;DR

This paper investigates the distribution properties of very short inversive congruential pseudorandom sequences modulo powers of two, introducing new bounds and discrepancy estimates using novel analytical techniques.

## Contribution

It presents a new bound on exponential sums and discrepancy estimates for short pseudorandom sequences, employing innovative methods not previously used in this context.

## Key findings

- Derived a new bound on exponential sums for short sequences
- Provided discrepancy estimates for inversive congruential sequences
- Applied novel analytical techniques with potential for broader applications

## 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 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.