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Asymptotics of second-order integral matrices lying in a given hyperbolic region and belonging to a given residue class

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Abstract

One obtains an asymptotic formula for the problem formulated in the title.

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Literature cited

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    A. M. Istamov, “Certain diophantine equations,” Tr. Samark. Gos. Univ.,235, 52–56(1973).

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    A. M. Istamov, “Number of distinct solutions of a diophantine equation,” Tr. Samark. Gos. Univ.,235, 56–61 (1973).

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

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    Yu. V. Linnik and B. F. Skubenko, “Asymptotic distribution of integral matrices of the third order,” Vestn. Leningr. Univ. Ser. Mat., No. 13, 25–36 (1964).

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    A. V. Malyshev, “Representations of integers by positive quadratic forms,” Tr. Mat. Inst. Akad. Nauk, Vol. 65, Moscow-Leningrad (1962).

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    A. G. Postnikov, Introduction to the Analytic Theory of Numbers [in Russian], Nauka, Moscow(1971).

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    B. F. Skubenko, “Distribution of integral matrices and the evaluation of the volume of the fundamental domain of the unimodular group of matrices,” Tr. Mat. Inst. Akad. Nauk,80, 129–144 (1967).

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

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 93, pp. 25–29, 1980.

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Istamov, A.M. Asymptotics of second-order integral matrices lying in a given hyperbolic region and belonging to a given residue class. J Math Sci 19, 1085–1088 (1982). https://doi.org/10.1007/BF01085124

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Keywords

  • Asymptotic Formula
  • Residue Class
  • Hyperbolic Region
  • Integral Matrice