Stability of the local gamma factor arising from the doubling method

Abstract

Let G be either a symplectic group or an orthogonal group over a local non-archimedean field F of characteristic zero. We consider the local gamma factor, associated to an irreducible admissible representation π of G, by the doubling method of Piatetski-Shapiro and Rallis ([PS.R.], [G.PS.R.], [L.R.]). Denote this gamma factor by γ (π, χ, s, ψ), where χ is a character of F ∗, and ψ is a fixed non-trivial character of F . In this paper we prove