A note on local densities of quadratic forms

Abstract

Let L, M be regular quadratic lattices over Z p . The local density α p (L, M ) is an important invariant in the theory of representation of quadratic forms and they appear naturally in Fourier coefficients of Eisenstein series. In spite of the importance we knew little except the case when either L = M or rk L = 1 and M is unimodular. Evaluating them is a laborious task.