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Zeta Integrals, Schwartz Spaces and Local Functional Equations

  • Book
  • © 2018

Overview

Authors:
  1. Wen-Wei Li

    1. Beijing International Center for Mathematical Research, Peking University, Beijing, China

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  • Offers a clearly written, timely addition to the literature
  • Provides concrete results complementing the more philosophical ideas of
  • Sakellaridis Reviews many recent results and reformulates them in a more natural form

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2228)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Wen-Wei Li
    Pages 1-20

  3. Geometric Background

    • Wen-Wei Li
    Pages 21-34

  4. Analytic Background

    • Wen-Wei Li
    Pages 35-44

  5. Schwartz Spaces and Zeta Integrals

    • Wen-Wei Li
    Pages 45-64

  6. Convergence of Some Zeta Integrals

    • Wen-Wei Li
    Pages 65-74

  7. Prehomogeneous Vector Spaces

    • Wen-Wei Li
    Pages 75-92

  8. The Doubling Method

    • Wen-Wei Li
    Pages 93-114

  9. Speculation on the Global Integrals

    • Wen-Wei Li
    Pages 115-131

  10. Back Matter

    Pages 133-141
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Keywords

About this book

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.


Reviews

“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 book accessible to a wider audience of mathematicians.” (Dubravka Ban, Mathematical Reviews, August, 2019)

Authors and Affiliations

  • Beijing International Center for Mathematical Research, Peking University, Beijing, China

    Wen-Wei Li

About the author

Wen-Wei Li received his Ph.D in Mathematics from Université Paris-Diderot in 2011. He is currently a Professor of the Beijing International Center of Mathematical Research, Peking University. His research is mainly focused on the theory of representation and automorphic forms.

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