Skip to main content
Log in

Asymptotic distribution of n-th-order integral matrices belonging to a given residue class

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

One obtains an asymptotic formula for the number of n-th-order integral matrices which belongs to a given domain of the discriminant surface and to a given residue class.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. Yu. V. Linnik, Ergodic Properties of Algebraic Fields, Springer-Verlag, New York (1968).

    Google Scholar 

  2. Yu. V. Linnik and B. F. Skubenko, “The asymptotic distribution of third-order integral matrices,” Vestn. Leningr. Univ., Ser. Mat. Mekh. Astron., No. 13(3), 25–36 (1964).

    Google Scholar 

  3. A. V. Malyshev, “On the representation of integers by positive quadratic forms,” Tr. Mat. Inst. Akad. Nauk SSSR,65 (1962).

  4. B. F. Skubenko, “On the distribution of integral matrices and the computation of the volume of the fundamental domain of a unimodular group of matrices,” Tr. Mat. Inst. Akad. Nauk SSSR,80, 129–144 (1967).

    Google Scholar 

  5. N. G. Chebotarev, The Theory of Lie Groups [in Russian], GITTL, Moscow (1940).

    Google Scholar 

  6. A. M. Istamov, “The asymptotic behavior of second-order integral matrices lying in a given hyperbolic region and belonging to a given residue class,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,93, 25–29 (1980).

    Google Scholar 

  7. E. V. Podsypanin, “Distribution of integral points on the determinant surface,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,93, 30–40 (1980).

    Google Scholar 

Download references

Authors

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 85–111, 1981.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Istamov, A.M. Asymptotic distribution of n-th-order integral matrices belonging to a given residue class. J Math Sci 25, 1030–1051 (1984). https://doi.org/10.1007/BF01680827

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01680827

Keywords

Navigation