Modular forms of degree <i>n</i> and representation by quadratic forms

Abstract

Let A (m) , B (n) be positive definite integral matrices and suppose that B is represented by A over each p-adic integers ring Z p . Using the circle method or theory of modular forms in case of n = 1, B , if sufficiently large, is represented by A provided that m ≥ 5. The approach via the theory of modular forms has been extended by [7] to Siegel modular forms to obtain a partial result in the particular case when n = 2, m ≥ 7.