Explicit Formulas for the Waldspurger and Bessel Models

Bump, Daniel; Friedberg, Solomon; Furusawa, Masaaki

Explicit Formulas for the Waldspurger and Bessel Models

Authors

Bump, Daniel

Friedberg, Solomon

Furusawa, Masaaki

Description

In this paper we will study certain models of irreducible admissible representations of the split special orthogonal group $SO(2n+1)$ over a nonarchimedean local field. If $n=1$, these models were considered by Waldspurger. If $n=2$, they were considered by Novodvorsky and Piatetski-Shapiro \cite{NP}, who called them {\it Bessel models}. They arise from a variety of Rankin-Selberg integrals nad the resultos of this paper will naturally have applications to the study of L-functions. They also arise in the study of the theta correspondence between $SO(2n+1)$ and the double cover of $Sp(2n)$, and they will therefore be of importance in generalizing the work of Waldspurger. As a global application we consider the Eisenstein series on $SO(2n+1)$ formed with a cuspidal automorphic representation $π$ on $GL(n)$, and we show that its Bessel period (6.2) is essentially a product of L-series. This generalizes work of Böcherer and Mizumoto.
38 pages