Uniqueness of Rankin-Selberg periods

Abstract

Let $k$ be a local field of characteristic zero. Rankin-Selberg's local zeta integrals produce linear functionals on generic irreducible admissible smooth representations of $G{L}_n(k)\times G{L}_r(k)$, with certain invariance properties. We show that up to scalar multiplication, these linear functionals are determined by the invariance properties.

References in corpus (3)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Smooth Frechet Globalizations of Harish-Chandra Modules
• Almost linear Nash groups