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Zeta integrals, Schwartz spaces and local functional equations

Author: Wen-Wei Li
Publisher: Cham, Switzerland : Springer, 2018.
Series: Lecture notes in mathematics (Springer-Verlag), 2228.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Li, Wen-Wei, 1982-
Zeta integrals, Schwartz spaces and local functional equations.
Cham, Switzerland : Springer, [2018]
(DLC) 2018956575
(OCoLC)1050363493
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Wen-Wei Li
ISBN: 9783030012885 3030012883
OCLC Number: 1062360100
Description: 1 online resource (viii, 141 pages) : illustrations (some color)
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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2228.
Responsibility: Wen-Wei Li.

Abstract:

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.

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"The book is carefully written; it enables the reader to navigate through highly technical material. The overview of classical results and thorough presentation of the background material make the Read more...

 
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