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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 4, Pages 510–533 (Mi msb2034)  

This article is cited in 4 scientific papers (total in 4 papers)

The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form

E. P. Golubeva


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 $n=A\mathbf b^2+\mathbf{ac}$ 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.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:2, 507–532

Bibliographic databases:

UDC: 511.3
MSC: Primary 10E10; Secondary 10E25
Received: 14.04.1983

Citation: E. P. Golubeva, “The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form”, Mat. Sb. (N.S.), 123(165):4 (1984), 510–533; Math. USSR-Sb., 51:2 (1985), 507–532

Citation in format AMSBIB
\Bibitem{Gol84}
\by E.~P.~Golubeva
\paper The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 4
\pages 510--533
\mathnet{http://mi.mathnet.ru/msb2034}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=740676}
\zmath{https://zbmath.org/?q=an:0566.10039|0546.10045}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 2
\pages 507--532
\crossref{https://doi.org/10.1070/SM1985v051n02ABEH002872}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. P. Golubeva, “Representation of large numbers by ternary quadratic forms”, Math. USSR-Sb., 57:1 (1987), 43–56  mathnet  crossref  mathscinet  zmath
    2. O. M. Fomenko, “Distribution of lattice points on hyperboloids”, J. Math. Sci. (N. Y.), 129:3 (2005), 3910–3915  mathnet  crossref  mathscinet  zmath
    3. U. M. Pachev, “Representation of integers by isotropic ternary quadratic forms”, Izv. Math., 70:3 (2006), 587–604  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. E. P. Golubeva, “Random variables associated with the Farey tree”, J. Math. Sci. (N. Y.), 193:1 (2013), 32–39  mathnet  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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