In this paper we study the possibility of real zeros near s = 1 for the RankinSelberg L-functions L(s, f × g) and L(s, sym(g) × sym(g)), where f, g are newforms, holomorphic or otherwise, on the upper half plane H, and sym(g) denotes the automorphic form on GL(3)/Q associated to g by Gelbart and Jacquet ([GJ79]). We prove that the set of such zeros of these L-functions is the union of the corre...

We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. We show that the geometric Langlands conjecture for an irreducible unramified local system E of rank n on a curve implies the existence of automorphic sheaves corresponding to the universal deformation of E. Then we calculate the ‘scalar product’ of two aut...

In this paper we study the analytic properties of standard L-function attached to vector valued quaternionic modular forms using Rankin-Selberg method. This involves construction theta series, which obtain by applying some differential operators on Jacobi-theta series studied Krieg. Such are obtained from Howe-Weyl duality for pair Spn(C)×GL2n(C).