Contents

Let f be a primitive positive integral binary quadratic form of discriminant −D, and let rf (n) be the number of representations of n by f up to automorphisms of f.Inthis article, we give estimates and asymptotics for the quantity ∑ n≤x rf (n) β for all β ≥ 0 and uniformly in D = o(x). As a consequence, we get more-precise estimates for th