Explicit Formulas for the Waldspurger and Bessel Models

Details Explicit Formulas for the Waldspurger and Bessel Models Explicit Formulas for the Waldspurger and Bessel Models

1994-10-20

arxiv.org/abs/math/9410202v1

Mathematics

Representation Theory

38 pages

Scientific paper

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 $\pi$ on $GL(n)$, and we show that its Bessel period (6.2) is essentially a product of L-series. This generalizes work of B\"ocherer and Mizumoto.

Affiliated with

Also associated with

No associations

Rating

Explicit Formulas for the Waldspurger and Bessel Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Explicit Formulas for the Waldspurger and Bessel Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explicit Formulas for the Waldspurger and Bessel Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-677940