Zeta Integrals, Schwartz Spaces and Local Functional Equations

• Main Author: Li, Wen-Wei (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Lecture Notes in Mathematics, 2228
• Subjects: Topological groups.; Lie groups.; Harmonic analysis.; Number theory.; Topological Groups, Lie Groups.; Abstract Harmonic Analysis.; Number Theory.

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 cou...

Table of 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.