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Zeta Integrals, Schwartz Spaces and Local Functional Equations

  • Wen-Wei Li

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. Wen-Wei Li
    Pages 1-20
  3. Wen-Wei Li
    Pages 21-34
  4. Wen-Wei Li
    Pages 35-44
  5. Wen-Wei Li
    Pages 45-64
  6. Wen-Wei Li
    Pages 65-74
  7. Wen-Wei Li
    Pages 75-92
  8. Wen-Wei Li
    Pages 93-114
  9. Wen-Wei Li
    Pages 115-131
  10. Back Matter
    Pages 133-141

About this book

Introduction

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.

Keywords

Distinguished Representation Local Functional Equation Poisson Formula Schwartz Space Zeta Integral

Authors and affiliations

  • Wen-Wei Li
    • 1
  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-01288-5
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-01287-8
  • Online ISBN 978-3-030-01288-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site