Together with Cogdell, Piatetski-Shapiro and Shahidi, we proved earlier the existence of a weak functorial lift of a generic cuspidal representation of SO2n+1 to GL2n. Recently, Ginzburg, Rallis and Soudry obtained a more precise form of the lift using their integral representation technique, namely, the lift is an isobaric sum of cuspidal representations of GLni (more precisely, cuspidal repre...

We continue our study of the tempered spectrum of quasi-split classical groups. Here we examine the case of the special orthogonal groups of odd dimension. While this is the last of the classical groups to be examined, it is the first for which our results address the tempered spectrum whose supercuspidal support is an arbitrary maximal parabolic subgroup, as we describe below. We continue to s...

In this paper we prove a conjecture of Jacquet about supercuspidal representations of GLn(K ) distinguished by GLn(k), or by Un(k), for K a quadratic unramified extension of a non-Archimedean local field k.

Let F be a non-archimedean local field with odd residual characteristic. Let G be the group SL2(F ). We construct explicit Whittaker models for any supercuspidal representation of G with positive level.

This paper studies the Fourier expansion of Hecke-Maass eigenforms for GL(2,Q) of arbitrary weight, level, and character at various cusps. It is shown that the Fourier coefficients at a cusp satisfy certain very explicit multiplicativity relations. As an application, it is proved that a local representation of GL(2,Qp) which is isomorphic to a local factor of a global cuspidal automorphic repre...

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation π of a connected reductive p-adic group, subject to the assumption that π is obtained via induction from a representation of an open compact mod centre subgroup. We derive an integral formula for each spherical character belonging to the the basis. This formula involves integration of a part...