Geodesic
Means over orbits of multidimensional lattices
Matematičeskie zametki, Tome 58 (1995) no. 1, pp. 48-66.

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

Two transformation groups of arbitrary multidimensional lattices are constructed. We prove the coincidence of arithmetic means of $q$-th deviations of lattices for the orbits of these transformation groups. 
@article{MZM_1995_58_1_a4,
     author = {N. M. Dobrovol'skii},
     title = {Means over orbits of multidimensional lattices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {48--66},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a4/}
}
TY  - JOUR
AU  - N. M. Dobrovol'skii
TI  - Means over orbits of multidimensional lattices
JO  - Matematičeskie zametki
PY  - 1995
SP  - 48
EP  - 66
VL  - 58
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a4/
LA  - ru
ID  - MZM_1995_58_1_a4
ER  - 
%0 Journal Article
%A N. M. Dobrovol'skii
%T Means over orbits of multidimensional lattices
%J Matematičeskie zametki
%D 1995
%P 48-66
%V 58
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a4/
%G ru
%F MZM_1995_58_1_a4
N. M. Dobrovol'skii. Means over orbits of multidimensional lattices. Matematičeskie zametki, Tome 58 (1995) no. 1, pp. 48-66. http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a4/

[1] Roth K. F., “On irregularities of distribution”, Math., 1 (1954), 73–79 | MR | Zbl

[2] Schmidt W. M., “Irregularities of distribution, X”, Number Theory and Algebra, ed. H. Zassenhaus, Academic Press, New York, 1977 | Zbl

[3] Roth K. F., “On irregularities of distribution, IV”, Acta Arith., 37 (1980), 67–75 | MR | Zbl

[4] Chen W. W. L., “On irregularities of distribution”, Math., 27:2 (1980), 153–170 | MR | Zbl

[5] Chen W. W. L., “On irregularities of distribution, XI”, Quart. J. Math., 34 (1983), 257–279 | DOI | MR | Zbl

[6] Dobrovolskii N. M., “Effektivnoe dokazatelstvo teoremy Rota o kvadratichnom otklonenii”, UMN, 39:4 (1984), 155–156 | MR | Zbl

[7] Dobrovolskii N. M., Otsenki modifitsirovannykh setok Khemmersli–Rota, Dep. No. 1365-84, VINITI, 1984

[8] Dobrovolskii N. M., Vankova V. S., Munos M. Penton, “Algoritm postroeniya optimalnykh modifitsirovannykh setok Khemmersli–Rota”, Matem. modelirovanie v fiz.-tekhn. zadachakh, Priokskoe knizhnoe izd-vo, Tula, 1989, 92–95

[9] Dobrovolskii N. M., Vankova V. S., Novye otsenki dlya modifitsirovannykh setok Khemmersli–Rota, Dep. v VINITI No. 4992-V90, 1990

[10] Vankova V. S., Dobrovolskii N. M., “Ob odnom algoritme dlya mnogomernykh setok”, Tezisy dokl. nauchno-teor. konf. “Teoriya chisel i ee prilozh.”, Tashkent, 1990 | Zbl

[11] Vankova V. S., Dobrovolskii N. M., Esayan A. R., O preobrazovaniyakh mnogomernykh setok, Dep. v VINITI No. 447-91, 1991 | Zbl

[12] Vankova V. S., Otsenka kvadratichnogo otkloneniya setok Kholtona, Dep. v VINITI 18.03.91, No. 1157-V91

[13] Vankova V. S., Kvadratichnoe otklonenie setok Fora–Chena, Dep. v VINITI 21.11.91, No. 4372-I91

[14] Vankova V. S., Ob algoritmakh poiska optimalnykh setok Khemmersli–Rota i Kholtona, Dep. v VINITI 21.11.91, No. 4371-V91

[15] Vankova V. S., Mnogomernye teoretiko-chislovye setki, Diss. ...kand. fiz.-matem. nauk, Mosk. pedagogich. gosud. un-t, M., 1992

[16] Vankova V. S., “O kvadratichnom otklonenii $q$-regulyarnykh $p$-ichnykh setok”, Tezisy dokl. mezhdunar. konf. “Sovr. problemy teorii chisel”, Tula, 1993, 24

[17] Dobrovolskii N. M., “Gruppy preobrazovanii mnogomernykh setok”, Tezisy dokl. mezhdun. konf. “Sovrem. problemy teorii chisel”, Tula, 1993, 46