On the distribution of reduced indefinite binary quadratic forms with the condition of first coefficients divisibility in residue classes
Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 139-150.

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

In this paper we generalize some B. F. Skubenko and autor results on the asymptotic distribution of integer indefinite binary quadratic forms obtained with the discrete ergodic method.
Keywords: asymptotic distribution of binary quadratic form, vector-matrix of the second order discrete ergodic method.
@article{CHEB_2013_14_2_a12,
     author = {U. M. Pachev},
     title = {On the distribution of reduced indefinite binary quadratic forms with the condition of first coefficients divisibility in residue classes},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {139--150},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a12/}
}
TY  - JOUR
AU  - U. M. Pachev
TI  - On the distribution of reduced indefinite binary quadratic forms with the condition of first coefficients divisibility in residue classes
JO  - Čebyševskij sbornik
PY  - 2013
SP  - 139
EP  - 150
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a12/
LA  - ru
ID  - CHEB_2013_14_2_a12
ER  - 
%0 Journal Article
%A U. M. Pachev
%T On the distribution of reduced indefinite binary quadratic forms with the condition of first coefficients divisibility in residue classes
%J Čebyševskij sbornik
%D 2013
%P 139-150
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a12/
%G ru
%F CHEB_2013_14_2_a12
U. M. Pachev. On the distribution of reduced indefinite binary quadratic forms with the condition of first coefficients divisibility in residue classes. Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 139-150. http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a12/

[1] Linnik Yu. V., Ergodicheskie svoistva algebraicheskikh polei, Izd-vo Leningr. un-ta, L., 1967 | MR | Zbl

[2] Skubenko B. F., “Asimptoticheskoe raspredelenie tselykh tochek na odnopolostnykh giperboloidakh i ergodicheskie teoremy”, Izvestiya AN SSSR. Ser. Matematika, 26:5 (1962), 721–752 | MR | Zbl

[3] Pachev U. M., “O chisle privedennykh tselochislennykh neopredelennykh binarnykh kvadratichnykh form s usloviem delimosti pervykh koeffitsientov”, Chebyshevskii sbornik, 4:3(7) (2003), 92–105 | MR | Zbl

[4] Linnik Yu. V., Izbrannye trudy. Teoriya chisel. Ergodicheskii metod i L-funktsii, Nauka, L., 1979 | MR | Zbl

[5] Pachev U. M., “Obzor issledovanii po diskretnomu ergodicheskomu metodu v teorii chisel”, Chebyshevskii sbornik, 11:1(33) (2010), 217–233 | MR | Zbl

[6] Pachev U. M., “O raspredelenii privedennykh polozhitelnykh binarnykh kvadratichnykh form s usloviem delimosti pervykh koeffitsientov po klassam vychetov”, Uchenye zap. Orlovskogo gos. un-ta, 2012, no. 6(50), 177–182

[7] Malyshev A. V., Pachev U. M., “Ob arifmetike matrits vtorogo poryadka”, Zap. nauch. sem. LOMI, 93, 1980, 43–86

[8] Venkov B. A., Elementarnaya teoriya chisel, ONTI, M.–L., 1937

[9] Malyshev A. V., Nguen Ngor Goi, “O raspredelenii tselykh tochek na nekotorykh odnopolostnykh giperboloidakh”, Zap. nauch. sem. LOMI, 121, 1983, 83–93 | Zbl

[10] Malyshev A. V., Shirokov B. M., “Novoe dokazatelstvo klyuchevoi lemmy diskretnogo ergodicheskogo metoda dlya vektor-matrits vtorogo poryadka”, Vestn. Leningrad. un-ta. Seriya 1, 1991, no. 2, 34–40

[11] Bachman P., Die Arithmetik der quadratischen Formen, Teubner, Leipzig, 1898 | Zbl