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

László Mérai | Zendy; Igor E. Shparlinski | Zendy

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

Author(s) -

László Mérai,

Igor E. Shparlinski

Publication year - 2019

Publication title -

mathematics of computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.95

H-Index - 103

eISSN - 1088-6842

pISSN - 0025-5718

DOI - 10.1090/mcom/3467

Subject(s) - mathematics , pseudorandom number generator , modulo , pseudorandomness , distribution (mathematics) , exponential function , discrete mathematics , combinatorics , value (mathematics) , upper and lower bounds , algorithm , statistics , mathematical analysis

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.

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