The Bessel Period Functional on SO(5): The Nontempered Case

Abstract

For automorphic representations in the nontempered cuspidal spectrum of ${\mathrm{SO}}_5$, we prove the refined Gan-Gross-Prasad conjecture by establishing a precise Bessel period formula, in which the square of the global Bessel period is expressed as an Euler product of regularized local Bessel period integrals of matrix coefficients.

arXiv comment38 pages

References in corpus (3)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• The Whittaker period formula on Metaplectic SL(2)
• The non-tempered theta 10 Arthur parameter and Gross-Prasad Conjectures

Cited by in corpus (4)

• A proof of the refined Gan--Gross--Prasad conjecture for non-endoscopic Yoshida lifts
• On fundamental Fourier coefficients of Siegel cusp forms of degree 2
• Spectral average of central values of automorphic L-functions for holomorphic cusp forms on SO_0(m,2) II
• Newforms of Saito-Kurokawa lifts