Abstract In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups p -adic general linear groups indexed by nonnegative integers and established the theory local newforms for irreducible generic representations. this paper, we extend their results to all To do this, define new certain tuples integers. For proof, introduce Rankin–Selberg integrals Speh

We use Poincare series for massive Maass-Jacobi forms to define a "massive theta lift", and apply it the examples of constant function modular invariant j-function, with Siegel-Narain as integration kernel. These integrals are deformations known one-loop string threshold corrections. Our lifts fall off exponentially, so some Rankin-Selberg finite without Zagier renormalization.

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...

The Rankin-Selberg convolution is usually normalized by the multiplication of a zeta factor. One naturally expects that the non-normalized convolution will have poles where the zeta factor has zeros, and that these poles will have the same order as the zeros of the zeta factor. However, this will only happen if the normalized convolution does not vanish at the zeros of the zeta factor. In this ...

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).