We give a construction of a wide class of modular symbols attached to reductive groups. As an application we construct a p-adic distribution interpolating the special values of the twisted Rankin-Selberg L-function attached to cuspidal automorphic representations π and σ of GLn and GLn−1 over a number field k. If π and σ are ordinary at p, our distribution is bounded and gives rise to a p-adic ...

We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. Our main result is local, its classical counterpart is the RankinSelberg computation of convolution of two Hecke eigenforms with an Eisenstein series. For n = 2 we apply it to prove a global result that gives a geometric version of the computation of the sc...

Duke and Kowalski in [6] derive a large sieve inequality for automorphic forms on GL(n) via the Rankin-Selberg method. We give here a partial complement to this result: using some explicit geometry of fundamental regions, we prove a large sieve inequality yielding sharp results in a region distinct to that in [6]. As an application, we give a generalization to GL(n) of Duke’s multiplicity theor...