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Asymptotic distribution of classes of positive binary quadratic forms with conditions of divisibility of coefficients

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Abstract

Asymptotic formulas for the number of classes of positive binary quadratic forms with conditions of divisibility of extreme coefficients are obtained by the discrete ergodic method.

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References

  1. Yu. V. Linnik, Ergodic Properties of Algebraic Fields [in Russian], Leningrad (1967).

  2. Yu. V. Linnik, “Asymptotic distribution of reduced binary quadratic forms in relation to Lobachevsky geometries. I–III,” Vestn. Leningr. Univ., No. 2, 3–23; No. 5, 3–32; No. 8, 15–27 (1955).

  3. A. V. Malyshev and U. M. Pachev, “On the number of classes of integer-valued positive binary forms whose arithmetic minimum is divisible by a given number,” in: Algebra and Theory of Numbers, No. 4, Nalchik (1979), 53–67.

  4. U. M. Pachev, “On the distribution of integral points on certain two-sheeted hyperboloids,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 93, 87–141 (1980).

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  5. U. M. Pachev, “On the number of classes of Gaussian genus whose arithmetic minimum is divisible by the square of a given odd number,” Mat. Zametki, 55, No. 2, 118–127 (1994).

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 123–130, 2005.

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Pachev, U.M. Asymptotic distribution of classes of positive binary quadratic forms with conditions of divisibility of coefficients. J Math Sci 146, 5717–5722 (2007). https://doi.org/10.1007/s10958-007-0387-8

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  • DOI: https://doi.org/10.1007/s10958-007-0387-8

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