Geodesic
Optimization of boundaries of remains for bounded remainder sets on two-dimensional torus
Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 9-17.

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

We consider two-dimensional bounded remainder sets, which are constructed by a hexagonal developmant of the torus. Also, we find optimization of boundaries for these sets.
Keywords: bounded remainder sets, distribution of fractional parts, toric development, exchanged domains, three-dimensional metric. 
@article{CHEB_2013_14_1_a1,
     author = {A. A. Abrosimova and D. A. Blinov and T. V. Polyakova},
     title = {Optimization of boundaries of remains for bounded remainder sets on two-dimensional torus},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {9--17},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a1/}
}
TY  - JOUR
AU  - A. A. Abrosimova
AU  - D. A. Blinov
AU  - T. V. Polyakova
TI  - Optimization of boundaries of remains for bounded remainder sets on two-dimensional torus
JO  - Čebyševskij sbornik
PY  - 2013
SP  - 9
EP  - 17
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a1/
LA  - ru
ID  - CHEB_2013_14_1_a1
ER  - 
%0 Journal Article
%A A. A. Abrosimova
%A D. A. Blinov
%A T. V. Polyakova
%T Optimization of boundaries of remains for bounded remainder sets on two-dimensional torus
%J Čebyševskij sbornik
%D 2013
%P 9-17
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a1/
%G ru
%F CHEB_2013_14_1_a1
A. A. Abrosimova; D. A. Blinov; T. V. Polyakova. Optimization of boundaries of remains for bounded remainder sets on two-dimensional torus. Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 9-17. http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a1/

[1] Hecke E., “Eber Analytische Funktionen und die Verteilung von Zahlen mod. eins”, Math. Sem. Hamburg. Univ., 1 (1921), 54—76 | DOI | MR

[2] Kesten H., “On a conjecture of Erdös and Szüsz related to uniform distribution mod 1”, Acta Arithmetica, 12 (1966), 193—212 | MR | Zbl

[3] Shutov A. V., “Optimalnye otsenki v probleme raspredeleniya drobnykh dolei na mnozhestvakh ogranichennogo ostatka”, Vestnik SamGU. Estestvennonauchnaya seriya, 5:3 (2007), 112—121

[4] Liardet P., “Regularities of distribution”, Compositio Math., 61 (1987), 267—293 | MR | Zbl

[5] Rauzy G., “Nombres algébriques et substitutions”, Bull. Soc. Math. France, 110 (1982), 147—178 | MR | Zbl

[6] Szüsz R., “Über die Verteilung der Vielfachen einer komplexen Zahl nach dem Modul des Einheitsquadrats”, Acta Math. Acad. Sci. Hungar., 5 (1954), 35—39 | DOI | MR | Zbl

[7] Zhuravlev V. G., “Razbieniya Rozi i mnozhestva ogranichennogo ostatka”, Zapiski nauchnykh seminarov POMI, 322, 2005, 83—106 | Zbl

[8] Zhuravlev V. G., “Mnogomernoe obobschenie teoremy Gekke”, Algebra i analiz, 24:1 (2012), 1—33

[9] Abrosimova A. A., “Mnozhestva ogranichennogo ostatka na dvumernom tore”, Chebyshevskii sbornik, 12:4(40) (2011), 15—23 | MR