On normal lattice configurations and simultaneously normal numbers

Mordechay B. Levin

doi:10.5802/jtnb.335

On normal lattice configurations and simultaneously normal numbers

Mordechay B. Levin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let q, q₁,..., q_s ≥ 2 be integers, and let α₁, α₂,... be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence (Formula Presented) coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences (Formula Presented) in s-dimensional unit cube (s,M,N = 1, 2,...). We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Formula Presented) (Korobov’s problem).

Original language	English
Pages (from-to)	483-527
Number of pages	45
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	13
Issue number	2
DOIs	https://doi.org/10.5802/jtnb.335
State	Published - 2001

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© Université Bordeaux 1, 2001, tous droits réservés.

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abstract = "Let q, q1,..., qs ≥ 2 be integers, and let α1, α2,... be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence (Formula Presented) coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences (Formula Presented) in s-dimensional unit cube (s,M,N = 1, 2,...). We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Formula Presented) (Korobov{\textquoteright}s problem).",

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N2 - Let q, q1,..., qs ≥ 2 be integers, and let α1, α2,... be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence (Formula Presented) coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences (Formula Presented) in s-dimensional unit cube (s,M,N = 1, 2,...). We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Formula Presented) (Korobov’s problem).

AB - Let q, q1,..., qs ≥ 2 be integers, and let α1, α2,... be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence (Formula Presented) coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences (Formula Presented) in s-dimensional unit cube (s,M,N = 1, 2,...). We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Formula Presented) (Korobov’s problem).

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On normal lattice configurations and simultaneously normal numbers

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