Explicit formulas for the waldspurger and bessel models |
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Authors: | Daniel Bump Solomon Friedberg Masaaki Furusawa |
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Institution: | (1) Department of Mathematics, Stanford University, 94305-2125 Stanford, CA, USA;(2) Department of Mathematics, University of California Santa Cruz, 95064 Santa Cruz, CA, USA;(3) Department of Mathematics, Boston College, 02167-3806 Chestnut Hill, MA, USA;(4) Department of Mathematics, The Johns Hopkins University, 21218 Baltimore, MD, USA |
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Abstract: | This paper studies certain models of irreducible admissible representations of the split special orthogonal group SO(2n+1) over a nonarchimedean local field. Ifn=1, these models were considered by Waldspurger. Ifn=2, they were considered by Novodvorsky and Piatetski-Shapiro, who called them Bessel models. In the works of these authors, uniqueness of the models is established; in this paper functional equations and explicit formulas for them are obtained. As a global application, the Bessel period of the Eisenstein series on SO(2n+1) formed with a cuspidal automorphic representation π on GL(n) is computed—it is shown to be a product of L-series. This generalizes work of Böcherer and Mizumoto forn=2 and base field ?, and puts it in a representation-theoretic context. In an appendix by M. Furusawa, a new Rankin-Selberg integral is given for the standardL-function on SO(2n+1)×GL(n). The local analysis of the integral is carried out using the formulas of the paper. |
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