Vanishing of certain equivariant distributions on p-adic spherical spaces, and non-vanishing of spherical Bessel functions

Abstract

We prove vanishing of distribution on p-adic spherical spaces that are equivariant with respect to a generic character of the nilradical of a Borel subgroup and satisfy a certain condition on the wave-front set. We deduce from this non-vanishing of spherical Bessel functions for Galois symmetric pairs.

9 pages. v2: extended version, to appear in IMRN

References in corpus (3)

• On an analogue of the Ichino--Ikeda conjecture for Whittaker coefficients on the metaplectic group
• z-Finite distributions on p-adic groups
• Vanishing of certain equivariant distributions on spherical spaces

Cited by in corpus (2)

• z-Finite distributions on p-adic groups
• Vanishing of certain equivariant distributions on spherical spaces