â€” We prove that the Dirichlet series of Rankinâ€“Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree n and weight k > n/2 has meromorphic continuation to C. Moreover, we show that the Petersson product of any pair of squareâ€“integrable modular forms of weight k > n/2 may be expressed in terms of the residue at s =â€¦ (More)

he was finally able to prove the two well-known elementary properties of Î¶(s), I mentioned before. The functional equation (3) is not trivial; in fact it follows (for instance) from a quite deep analytical result, called Poisson summation formula, which asserts that if f is a smooth function with rapid decay on R (actually, these hypotheses could beâ€¦ (More)