Boundedness of automorphic 𝐿–functions in vertical strips

2000/09/18 by Stephen Gelbart, Freydoon Shahidi · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Finite Group Theory Research

paper · pdf · doi:10.1090/s0894-0347-00-00351-9

openalex publication_date 2000/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

In this paper we prove the boundedness in vertical strips of finite width for all the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>–functions that appear in constant terms of Eisenstein series, under a certain natural assumption on local normalized intertwining operators. This result has been quite important in establishing recent cases of Langlands functoriality by Cogdell, Kim, Piatetski-Shapiro, and Shahidi, using converse theorems.

Citations

• On Euler Products and the Classification of Automorphic Representations I
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• The symmetric cube
• On Certain L-Functions
• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique
• Zeros of principal L-functions and random matrix theory
• Converse theorems for GLn, II
• Rankin-Selberg Convolutions
• On the Ramanujan Conjecture and Finiteness of Poles for Certain L- Functions
• A Proof of Langlands' Conjecture on Plancherel Measures; Complementary Series of -adic groups

Cited by

• Functorial products for GL2×GL3 and functorial symmetric cube for GL2
• A refined Poisson summation formula for certain Braverman-Kazhdan spaces
• Freydoon Shahidi [wikipedia]