Geodesic
Bounded remainder sets on the double covering of the Klein bottle
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 82-105 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The shift $\widetilde{\mathbb S}\colon\widetilde{\mathbb K}^2\to\widetilde{\mathbb K}^2$ on the double covering of the Klein bottle $\widetilde{\mathbb K}^2=\mathbb K^2\times\{\pm1\}$ is considered. This shift $\widetilde{\mathbb S}$ generates some tiling $\widetilde{\mathbb K}^2=\widetilde{\mathbb K}^2_0\sqcup\widetilde{\mathbb K}^2_1$ into two bounded remainder sets $\widetilde{\mathbb K}^2_0$ and $\widetilde{\mathbb K}^2_1$ with respect to the shift $\widetilde{\mathbb S}$. Two-sided estimates are proved for the deviation functions of these sets. 
@article{ZNSL_2014_429_a7,
     author = {V. G. Zhuravlev},
     title = {Bounded remainder sets on the double covering of the {Klein} bottle},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--105},
     year = {2014},
     volume = {429},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a7/}
}
TY  - JOUR
AU  - V. G. Zhuravlev
TI  - Bounded remainder sets on the double covering of the Klein bottle
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 82
EP  - 105
VL  - 429
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a7/
LA  - ru
ID  - ZNSL_2014_429_a7
ER  - 
%0 Journal Article
%A V. G. Zhuravlev
%T Bounded remainder sets on the double covering of the Klein bottle
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 82-105
%V 429
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a7/
%G ru
%F ZNSL_2014_429_a7
V. G. Zhuravlev. Bounded remainder sets on the double covering of the Klein bottle. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 82-105. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a7/

[1] V. G. Zhuravlev, “Razbieniya Rozi i mnozhestva ogranichennogo ostatka”, Zap. nauch. semin. POMI, 322, 2005, 83–106 | MR | Zbl

[2] V. G. Zhuravlev, “Perekladyvayuschiesya toricheskie razvertki i mnozhestva ogranichennogo ostatka”, Zap. nauch. semin. POMI, 392, 2011, 95–145 | MR

[3] V. G. Zhuravlev, “Mnogomernaya teorema Gekke o raspredelenii drobnykh dolei”, Algebra i analiz, 24:1 (2012), 95–130 | MR | Zbl

[4] V. G. Zhuravlev, “Moduli toricheskikh razbienii na mnozhestva ogranichennogo ostatka i sbalansirovannye slova”, Algebra i analiz, 24:4 (2012), 97–136 | MR | Zbl

[5] V. G. Zhuravlev, “Mnogogranniki ogranichennogo ostatka”, Matematika i informatika, K 75-letiyu so dnya rozhdeniya Anatoliya Alekseevicha Karatsuby, v. 1, Sovr. probl. matem., 16, MIAN, M., 2012, 82–102 | DOI | Zbl

[6] S. Grepstad, N. Lev, Sets of bounded discrepancy for multi-dimensional irrational rotation, 1 Apr. 2014, 39 pp., arXiv: 1404.0165v1[math.DS]

[7] A. Haynes, H. Koivusalo, Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices, 20 Feb. 2014, 11 pp., arXiv: 1402.2125v2[math.DS]

[8] R. Szüsz, “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

[9] G. Rauzy, “Ensembles à restes bornés”, Séminaire de théorie des nombres de Bordeaux, 1984, Exposé No. 24, 12 pp. | MR

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

[11] S. Ferenczi, “Bounded Remaider Sets”, Acta Arithmetica, 61:4 (1992), 319–326 | MR | Zbl

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

[13] V. G. Zhuravlev, “Odnomernye razbieniya Fibonachchi i indutsirovannye dvutsvetnye povoroty edinichnoi okruzhnosti”, Izv. RAN, ser. matem., 74:2 (2010), 65–108 | DOI | MR | Zbl

[14] A. A. Abrosimova, “Srednie znacheniya otklonenii dlya raspredeleniya tochek na tore”, Nauchnye vedomosti BelGU. Ser. Matematika. Fizika, 5:26 (2012), 5–11

[15] E. S. Fedorov, Nachala ucheniya o figurakh, M., 1953

[16] G. F. Voronoi, Sobranie sochinenii, v. 2, Kiev, 1952