Bessel identities in the Waldspurger correspondence over the real numbers
type: Item
instance of: scholarly article
title: Bessel identities in the Waldspurger correspondence over the real numbers
zbMATH Open document ID: 1064.22009
DOI: 10.1007/BF02786684
author: Ehud Moshe Baruch
author: Zhengyu Mao
published in: Israel Journal of Mathematics
publication date: 2005-05-03T00:00:00Z
review text: In this paper certain identities between Bessel functions attached to irreducible unitary representations of \(\text{PGL}_2 (\mathbb R)\) and those for the double cover of \(\text{SL}_2 (\mathbb R)\) are established. Then a correspondence between such representations is realized by these Bessel identities, it is just the Waldspurger correspondence. Several regularity theorems for Bessel distributions appearing in the relative trace formula are proved by using a classical result of Weber and Hardy on Fourier transforms of classical Bessel functions. This paper constitutes the local (real) spectral theory of the relative trace formula for the Waldspurger correspondence for which the global part was developed by Jacquet.
reviewed by: Na Jisheng
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 2164534
zbMATH Keywords: Bessel identity
zbMATH Keywords: Waldspurger correspondence
zbMATH Keywords: irreducible unitary representation
zbMATH Keywords: relative trace formula
MaRDI profile type: Publication
cites work: On Bessel distributions for \(GL_ 2\) over a \(p\)-adic field
cites work: On Bessel distributions for quasi-split groups
cites work: Central value of automorphic \(L\)-functions
cites work: Bessel identities in the Waldspurger correspondence over a p- adic field
cites work: Q3996745
cites work: Q5827353
cites work: Weil's representation and the spectrum of the metaplectic group
cites work: Q4118032
cites work: Q5222755
cites work: Automorphic forms on GL (2)
cites work: On the nonvanishing of some \(L\)-functions
cites work: Metaplectic forms
cites work: Q3741813
cites work: Q3215519
cites work: A note on the mean value of the zeta and \(L\)-functions. XII.
cites work: Whittaker models for real groups
cites work: The multiplicity one theorem for \(\mathrm{GL}_n\)
cites work: The L and \(\gamma\) factors for generic representations of GSp(4,k)\(\times GL(2,k)\) over a local nonarchimedean field k
cites work: Q4394703
cites work: Q5559954
cites work: Shimura and Shintani correspondences
cites work: Correspondances de Shimura et quaternions
cites work: Q3994337
cites work: Q4856171
full work available at URL: https://doi.org/10.1007/bf02786684
OpenAlex ID: W2061105616
description: scientific article; zbMATH DE number 2164534