On Petersson products of not necessarily cuspidal modular forms

Abstract

We show that Petersson products of any pair of elliptic modular forms of weight 1 2 and of any pair of Siegel modular forms of degree 2 and weight 1 have an expression as the residue of a Dirichlet series of Rankin–Selberg type. This generalizes a well-known property of cuspidal Petersson products.