On Dirichlet series whose coefficients are class numbers of binary quadratic forms

Abstract

For an integer d > 0 (resp. d < 0) let hd denote the number of Sl2(Z)-equivalence classes of primitive (resp. primitive positive-definite) integral binary quadratic forms of discriminant d. For where t and u are the smallest positive integral solutions of the equation t2 − du2 = 4 if d is a non-square and εd = 1 if d is a square.