This article is cited in 4 papers

On the asymptotics of the number of reduced integral quadratic forms with a condition of divisibility of the first coefficients

U. M. Pachev

Kabardino-Balkar State University

Abstract: For the quadratic forms mentioned in the title, we use the discrete ergodic method to obtain asymptotic formulas with remainders depending on the $L$-Dirichlet function $L(s,\chi)$ and its behavior under some hypotheses.

Keywords: discrete ergodic method, reduced binary quadratic form, divisibility of coefficients, second-order vector-matrix.

UDC: 511.512

Received: 20.09.2005

 English version: Siberian Mathematical Journal, 2007, 48:2, 300–310

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