Abstract:
Under the assumption of a nontrivial shift of the zeros of Dirichlet L-series with quadratic character, asymptotic formulas are obtained for the number of lattice points in arbitrary regions on the hyperboloid n=Ab2+ac belonging to given residue classes. A method for applying the results to the study of the distribution of lattice points on general second-order surfaces is outlined.
Bibliography: 19 titles.
Citation:
E. P. Golubeva, “The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form”, Math. USSR-Sb., 51:2 (1985), 507–532
\Bibitem{Gol84}
\by E.~P.~Golubeva
\paper The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 2
\pages 507--532
\mathnet{http://mi.mathnet.ru/eng/sm2034}
\crossref{https://doi.org/10.1070/SM1985v051n02ABEH002872}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=740676}
\zmath{https://zbmath.org/?q=an:0566.10039|0546.10045}
Linking options:
https://www.mathnet.ru/eng/sm2034
https://doi.org/10.1070/SM1985v051n02ABEH002872
https://www.mathnet.ru/eng/sm/v165/i4/p510
This publication is cited in the following 4 articles:
E. P. Golubeva, “Random variables associated with the Farey tree”, J. Math. Sci. (N. Y.), 193:1 (2013), 32–39
U. M. Pachev, “Representation of integers by isotropic ternary quadratic forms”, Izv. Math., 70:3 (2006), 587–604
O. M. Fomenko, “Distribution of lattice points on hyperboloids”, J. Math. Sci. (N. Y.), 129:3 (2005), 3910–3915
E. P. Golubeva, “Representation of large numbers by ternary quadratic forms”, Math. USSR-Sb., 57:1 (1987), 43–56
Citation in format AMSBIB
Contact us: