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Mathematics > Number Theory

arXiv:1812.08837 (math)
[Submitted on 20 Dec 2018 (v1), last revised 12 Jun 2019 (this version, v2)]

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

Authors:László Mérai, Igor E. Shparlinski
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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.
Subjects: Number Theory (math.NT)
Cite as: arXiv:1812.08837 [math.NT]
  (or arXiv:1812.08837v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1812.08837

Submission history

From: Igor Shparlinski [view email]
[v1] Thu, 20 Dec 2018 21:02:53 UTC (11 KB)
[v2] Wed, 12 Jun 2019 12:46:40 UTC (11 KB)
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