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 . In this
article, we give estimates and asymptotics for the quantity
∑n≤xrf(n)β for all
β≥0
and uniformly in
D=o(x). As a consequence, we get more-precise estimates for the
number of integers which can be written as the sum of two powerful numbers.
Article