Geodesic
A~probability estimate for the discrepancy of Korobov lattice points
Sbornik. Mathematics, Tome 212 (2021) no. 11, pp. 1571-1587

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Bykovskii (2002) obtained the best current upper estimate for the minimum discrepancy of the Korobov lattice points from the uniform distribution. We show that this estimate holds for almost all $s$-dimensional Korobov lattices of $N$ nodes, where $s\geqslant 3$, and $N$ is a prime number. Bibliography: 14 titles.
Keywords: Korobov lattice, uniform distribution, discrepancy from the uniform distribution, sums over sublattices. 
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     title = {A~probability estimate for the discrepancy of {Korobov} lattice points},
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A. A. Illarionov. A~probability estimate for the discrepancy of Korobov lattice points. Sbornik. Mathematics, Tome 212 (2021) no. 11, pp. 1571-1587. http://geodesic.mathdoc.fr/item/SM_2021_212_11_a2/