Geodesic
A structure formula for the sequence $\{n\theta\}$ and some of its applications in problems of number theory
Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 152-172.

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

@article{CHEB_2010_11_1_a15,
     author = {I. I. Il'yasov},
     title = {A structure formula for the sequence $\{n\theta\}$ and some of its applications in problems of number theory},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {152--172},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a15/}
}
TY  - JOUR
AU  - I. I. Il'yasov
TI  - A structure formula for the sequence $\{n\theta\}$ and some of its applications in problems of number theory
JO  - Čebyševskij sbornik
PY  - 2010
SP  - 152
EP  - 172
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a15/
LA  - ru
ID  - CHEB_2010_11_1_a15
ER  - 
%0 Journal Article
%A I. I. Il'yasov
%T A structure formula for the sequence $\{n\theta\}$ and some of its applications in problems of number theory
%J Čebyševskij sbornik
%D 2010
%P 152-172
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a15/
%G ru
%F CHEB_2010_11_1_a15
I. I. Il'yasov. A structure formula for the sequence $\{n\theta\}$ and some of its applications in problems of number theory. Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 152-172. http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a15/

[1] Veil G. (Weyl H.), “Über die Gleichverteilung von Zahlen mod. Eins”, Math. Ann., 77 (1916), 313–352 | MR | Zbl

[2] Vinogradov I. M., Osnovy teorii chisel, Nauka, M., 1978

[3] Keipers L., Niderreiter G., Ravnomernoe raspredelenie posledovatelnostei, Nauka, M., 1985

[4] Leng S., Vvedenie v teoriyu diofantovykh priblizhenii, Mir, M., 1970

[5] Perron O., Die Lehre von den Kettenbrüchen, Teubner, Leipzig–Berlin, 1929 | Zbl

[6] Ostrowski A., “Bemerkungen zur Theorie der Diophantischen Approximat”, Abh. Hamburg Universitet, 1 (1921), 77–98

[7] Behnke H., “Zur Theorie der diophantischen Approximationen”, Abh. Math. Semin. Humburg. Univ., 3 (1924), 261–318 | Zbl

[8] Khinchin A. Ya., Tsepnye drobi, Izd. 3-e, Fizmatgiz, M., 1961, 28–30

[9] Pashkovskii S., Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983

[10] Ilyasov I. I., “O strukture posledovatelnosti $\left\{n\theta \right\}$”, Teoriya neregulyarnykh krivykh v razlichnykh geometricheskikh prostranstvakh, Alma-Ata, 1979, 44–52

[11] Ilyasov I. I., “Ob odnom sposobe resheniya sravneniya pervoi stepeni”, Vestnik Aktyubinskogo gosudarstvennogo universiteta, 2006, no. 3, 14–15

[12] Ilyasov I. I., “Umnozhenie tsepnykh drobei na prostoe chislo”, Izvestiya Akademiya nauk Kazakhskoi SSR. Seriya fiziko-matematicheskaya, 1985, no. 3, 38–41

[13] Sleiter (Slater N. B.), “The distributions of the integers $N$ with $\{ \theta N\} \phi$”, Proc. Cambridge Phil. Soc., 46 (1950), 525–534 | MR | Zbl

[14] Florek (Florec K.), “Une remarque sur la reparatition des nombers $n\xi\pmod1$”, Colloc. Math., 2 (1951), 323–324

[15] Shosh (Sos V. T.), “On the distribution $\mod 1$ of the sequence $n\alpha $”, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 1 (1958), 127–134 | Zbl

[16] Shurani (Suranyi J.), “Über die Anordnung der Vielfachen einer reelen Zahl $\mod 1$”, Ann. Univ. Sci. Budapest. Eötvö Sect. Math., 1 (1958), 107–111 | MR | Zbl

[17] Sverchekovskii (Swierczkowski S.), “On successive setting of an arc on the circumference of a circle”, Fundam. Math., 46 (1958), 187–189 | MR