The first term identities for Eisenstein series
type: Item
instance of: scholarly article
title: The first term identities for Eisenstein series
zbMATH Open document ID: 0913.11021
published in: Journal of Number Theory
publication date: 1999-06-07T00:00:00Z
review text: The author studies the theory of Eisenstein series associated with maximal parabolic subgroups of \(Sp(2n)\) over a number field. These are functions of a single complex variable \(s\), and the author defines the ``largest'' singularity (measured by \(\text{Re}(s)\)). The subject of the investigation is the leading term considered as a linear functional. The Kudla-Rallis formula, itself an extension of the Siegel-Weil formula, can be considered as an identity between two such functionals. The author formulates a precise conjecture in a very general setting and proves this in certain cases. The last section is devoted to some local questions. The techniques used are mainly from the general theory of Eisenstein series, which the author develops in detail in this case.
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 1207966
zbMATH Keywords: Eisenstein series
zbMATH Keywords: maximal parabolic subgroups
zbMATH Keywords: number field
zbMATH Keywords: singularity
zbMATH Keywords: Kudla-Rallis formula
zbMATH Keywords: Siegel-Weil formula
author: Dihua Jiang
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
full work available at URL: jnth.1998.2223
OpenAlex ID: W2078090346
cites work: Q3328757
cites work: Canonical Extensions of Harish-Chandra Modules to Representations of G
cites work: Q4297091
cites work: The central critical value of a triple product \(L\)-function
cites work: Q4845624
cites work: Q4013401
cites work: Q4388249
cites work: Q3325944
cites work: Degenerate principal series for symplectic and odd-orthogonal groups
cites work: Degree 16 standard 𝐿-function of 𝐺𝑆𝑝(2)×𝐺𝑆𝑝(2)
cites work: Q3504296
cites work: A regularized Siegel-Weil formula: The first term identity
cites work: Q3497143
cites work: Q3786531
cites work: On the Weil-Siegel formula II.
cites work: On the degree 5 \(L\)-function for \(Sp(2)\)
cites work: On the functional equations satisfied by Eisenstein series
cites work: Spectral decomposition and Eisenstein series
cites work: Explicit constructions of automorphic \(L\)-functions
cites work: Q3778068
cites work: Weil representation. I. Intertwining distributions and discrete spectrum
cites work: Q5682517
cites work: Sur la formule de Siegel dans la théorie des groupes classiques
DOI: 10.1006/JNTH.1998.2223
description: scientific article; zbMATH DE number 1207966