Modular forms of degree n and representation by quadratic forms II

Abstract

Let S(m), T(n) be positive definite integral matrices and suppose that T is represented by S over each p-adic integer ring Zp. We proved arithmetically in [3] that T is represented by S over Z provided that m ≥ 2n + 3 and the minimum of T is sufficiently large. This guarantees the existence of at least one representation but does not give any asymptotic formula for the number of representations. To get an asymptotic formula we must employ analytic methods.