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

Format:

Book

Author/Creator:

Li, Wen-Wei, 1982- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2228.

Lecture Notes in Mathematics, 0075-8434 ; 2228

Language:

English

Subjects (All):

Topological groups.

Harmonic analysis.

Number theory.

Topological Groups, Lie Groups.

Abstract Harmonic Analysis.

Number Theory.

Local Subjects:

Topological Groups, Lie Groups.

Abstract Harmonic Analysis.

Number Theory.

Physical Description:

1 online resource (VIII, 141 pages 30 illustrations, 2 illustrations in color).

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2018.

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.

Other Format:

Printed edition:

ISBN:

9783030012885

Access Restriction:

Restricted for use by site license.