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Zeta Integrals, Schwartz Spaces and Local Functional Equations [electronic resource] / by Wen-Wei Li.

Author/Creator:
Li, Wen-Wei. author., Author,
Publication:
Cham : Springer International Publishing : Imprint: Springer, 2018.
Format/Description:
Book
1 online resource (VIII, 141 pages 30 illustrations, 2 illustrations in color)
Series:
Lecture Notes in Mathematics, 0075-8434 ; 2228
Lecture Notes in Mathematics, 0075-8434 ; 2228
Contained In:
Springer eBooks
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Subjects:
Topological Groups.
Harmonic analysis.
Number theory.
Local subjects:
Topological Groups, Lie Groups. (search)
Abstract Harmonic Analysis. (search)
Number Theory. (search)
System Details:
text file PDF
Summary:
This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.
Contents:
Introduction
Geometric Background
Analytic Background
Schwartz Spaces and Zeta Integrals
Convergence of Some Zeta Integrals
Prehomogeneous Vector Spaces
The Doubling Method
Speculation on the Global Integrals.
Contributor:
SpringerLink (Online service)
Other format:
Printed edition:
Printed edition:
ISBN:
9783030012885
Publisher Number:
10.1007/978-3-030-01288-5 doi
Access Restriction:
Restricted for use by site license.