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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Yu. V. Linnik, Ergodic Properties of Algebraic Fields [in Russian], Leningrad (1967).
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).
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.
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).
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).
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
- Quadratic Form
- Asymptotic Formula
- Asymptotic Distribution
- Prime Divisor
- Residue Class