Geodesic
The discrepancy of the Korobov lattice points
Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 446-465.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain substantially improved bounds for the discrepancy of the Korobov lattice points from the uniform distribution.
Keywords: uniform distribution, Korobov lattice points, lattice, relative minimum. 
@article{IM2_2012_76_3_a1,
     author = {V. A. Bykovskii},
     title = {The discrepancy of the {Korobov} lattice points},
     journal = {Izvestiya. Mathematics },
     pages = {446--465},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a1/}
}
TY  - JOUR
AU  - V. A. Bykovskii
TI  - The discrepancy of the Korobov lattice points
JO  - Izvestiya. Mathematics 
PY  - 2012
SP  - 446
EP  - 465
VL  - 76
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a1/
LA  - en
ID  - IM2_2012_76_3_a1
ER  - 
%0 Journal Article
%A V. A. Bykovskii
%T The discrepancy of the Korobov lattice points
%J Izvestiya. Mathematics 
%D 2012
%P 446-465
%V 76
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a1/
%G en
%F IM2_2012_76_3_a1
V. A. Bykovskii. The discrepancy of the Korobov lattice points. Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 446-465. http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a1/

[1] L. Kuipers, H. Niederreiter, Uniform distribution of sequences, Wiley, New York–London–Sydney–Toronto, 1974 | MR | MR | Zbl | Zbl

[2] N. M. Korobov, “O priblizhennom vychislenii kratnykh integralov”, Dokl. AN SSSR, 124:6 (1959), 1207–1210 | MR | Zbl

[3] E. Hlawka, “Zur angenäherten Berechnung mehrfacher Integrale”, Monatsh. Math., 66:2 (1962), 140–151 | DOI | MR | Zbl

[4] N. M. Korobov, Teoretiko-chislovye metody v priblizhennom analize, MTsNMO, M., 2004 | MR | Zbl

[5] H. Niederreiter, “Existence of good lattice points in the sense of Hlawka”, Monatsh. Math., 86:3 (1978), 203–219 | DOI | MR | Zbl

[6] W. M. Schmidt, “Irregularities of distribution. VII”, Acta Arith., 21 (1972), 45–50 | MR | Zbl

[7] M. Drmota, R. F. Tichy, Sequences, discrepancies and applications, Lecture Notes in Math., 1651, Springer-Verlag, Berlin, 1997 | DOI | MR | Zbl

[8] M. M. Skriganov, “Constructions of uniform distributions in terms of geometry of numbers”, Algebra i analiz, 6:3 (1994), 200–230 | MR | Zbl

[9] V. A. Bykovskii, “On the error of number-theoretic quadrature formulas”, Dokl. Math., 67:2 (2003), 175–176 | MR | Zbl

[10] G. Larcher, “On the distribution of sequences connected with good lattice points”, Monatsh. Math., 101:2 (1986), 135–150 | DOI | MR | Zbl

[11] G. F. Voronoi, Sobranie sochinenii v 3-kh tomakh, v. 1, Izd-vo AN USSR, Kiev, 1952 | MR | Zbl

[12] H. Minkowski, “Généralisation de la théorie des fractions continues”, Ann. Sci. École Norm. Sup. (3), 13 (1896), 41–60 | MR | Zbl

[13] H. Niederreiter, “Quasi-Monte Carlo methods and pseudo-random numbers”, Bull. Amer. Math. Soc., 84:6 (1978), 957–1041 | DOI | MR | Zbl

[14] N. S. Bakhvalov, “O priblizhennom vychislenii kratnykh integralov”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1959, no. 4, 3–18 | MR | Zbl