Counting Square Discriminants

2013/07/24 by Thomas A. Hulse, Hulse, Thomas A., E. Mehmet Kıral +5
Mathematics · #11 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11

paper · pdf · doi:10.48550/arxiv.1307.6606

arxiv created 2015/08/06 · arxiv updated 2015/08/10

Abstract

Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions on the size of their coefficients. We accomplish this by investigating the analytic properties of a certain double Dirichlet series, which is a shifted convolution sum of certain classical automorphic forms.

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