The base change \(L\)-function for modular forms and beyond endoscopy
type: Item
instance of: scholarly article
title: The base change \(L\)-function for modular forms and beyond endoscopy
zbMATH Open document ID: 1305.11045
author: Paul-James White
published in: Journal of Number Theory
publication date: 2014-08-27T00:00:00Z
reviewed by: Ivan Matić
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 6334890
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: beyond endoscopy
zbMATH Keywords: trace formula
MaRDI profile type: Publication
full work available at URL: j.jnt.2014.01.006
OpenAlex ID: W2041797367
cites work: Q5488002
cites work: A strengthening of the GL(2) converse theorem
cites work: The geometry and cohomology of some simple Shimura varieties. With an appendix by Vladimir G. Berkovich
cites work: The functional equation and beyond endoscopy
cites work: Automorphic forms on GL (2)
cites work: A relative trace formula proof of the Petersson trace formula
cites work: Q3887686
cites work: Q4662310
cites work: Q4781493
cites work: Beyond Endoscopy and special forms on GL(2)
DOI: 10.1016/J.JNT.2014.01.006
review text: In the paper under review, the author studies \(L\)-functions arising from base change in the case of a modular form using the trace formula, building on ideas of \textit{R. P. Langlands} [in: Contributions to automorphic forms, geometry, and number theory. Johns Hopkins University, Baltimore, USA, 2002. Baltimore, MD: Johns Hopkins University Press. 611--697 (2004; Zbl 1078.11033)] and \textit{P. Sarnak} [``Comments on Robert Langlands lecture: `Endoscopy and Beyond' '', Letter (2001)] on the \textit{beyond endoscopy} program.NEWLINENEWLINEIn the case of quadratic base change for real fields, the introduced methods enable the author to provide a new proof of the absolute convergence and analytic continuation of the studied \(L\)-functions in appropriate right half planes.
description: scientific article; zbMATH DE number 6334890