An explicit inversion formula for the $p$-adic Whittaker transform on ${\text{GL}}_n({\mathbb{Q}}_p)$

Abstract

Whittaker functions on non-archimedean fields were first introduced in the work of Jacquet, and they were characterized explicitly by Shintani. We obtain an explicit inversion formula and a Plancherel formula for the $p$-adic Whittaker transform on ${\text{GL}}_n({\mathbb{Q}}_p)$. As an application, integral representations are obtained for the local factors of certain symmetric power $L$-functions.

12 pages

References in corpus (1)

• Formule de Plancherel pour les fonctions de Whittaker sur un groupe réductif $p$-adique

Cited by in corpus (1)

• From partition identities to a combinatorial approach to explicit Satake inversion