On Petersson products of not necessarily cuspidal modular forms (Q863954)

The paper considers elliptic modular forms of weight \(k=\frac{1}{2}\) and Siegel modular forms of degree 2 and weight \(k=1\). The Petersson product of any pair of such forms converges and can be expressed in terms of the residue at \(s=k\) of a suitable Dirichlet series of Rankin-Selberg type. This extends a classical property of the Petersson inner product for cusp forms.