Indefinite quadratic forms and Eisenstein series, Forum Math

Abstract. We use geometric algebra and the theory of automorphic forms to realize the theta series attached to an indefinite quadratic form as the sum of a specific Eisenstein series and an L2-function. From this we obtain explicit formulas for the measure of the representation of an integer by an indefinite quadratic form. §Introduction. In this paper we study, from the point of view of automorphic forms, the rep-resentation number of indefinite quadratic forms. In [12], the second author used similar techniques for positive definite quadratic forms. In that case, much of the local theory was similar, but the global automorphic theory was much simpler. A