Let
be a a negative discriminant and let T vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant
. We prove an asymptotic formula for
for the average over T of the number of representations of T by an integral positive definite quaternary quadratic form and obtain bounds for averages of
... [Show full abstract] Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic estimate from below on the number of binary forms of fixed discriminant which are represented by a given quaternary form. In particular, we can show that for growing d a positive proportion of the binary quadratic forms of discriminant is represented by the given quaternary quadratic form.
