Asymptotic distribution of integer-valued binary forms of a~fixed discriminant
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 26-40
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Under the assumption on the boundary of the zeros of the Dirichlet $L$-functions, one obtains a refinement of the results of Yu. V. Linnik and B. F. Skubenko on the uniformity of the distribution of integral points on the hyperboloids
$$
D=b^2-ac,\qquad(D\ne0).
$$
As a corollary one obtains the asymptotic behavior of the number of reduced indefinite binary quadratic forms of discriminant $4D$.
@article{ZNSL_1981_112_a1,
author = {E. P. Golubeva},
title = {Asymptotic distribution of integer-valued binary forms of a~fixed discriminant},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {26--40},
publisher = {mathdoc},
volume = {112},
year = {1981},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a1/}
}
E. P. Golubeva. Asymptotic distribution of integer-valued binary forms of a~fixed discriminant. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 26-40. http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a1/