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Eisenstein Series and Applications

  • Book
  • © 2008

Overview

Editors:
  1. Wee Teck Gan

    1. Department of Mathematics, University of California, San Diego, La Jolla, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Stephen S. Kudla

    1. Department of Mathematics, University of Toronto, Toronto, Canada

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    You can also search for this editor in PubMed   Google Scholar

  3. Yuri Tschinkel

    1. Courant Institute of Mathematical Sciences, New York University, New York, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Brings together contributions from diverse areas, exposing users of Eisenstein series to a variety of important applications
  • Focuses on the common structural properties of Eisenstein series as applied to several recent developments in arithmetic: Arakelov intersection theory on Shimura varieties, special values of L-functions and Iwasawa theory, and equidistribution of rational/integer points on homogeneous varieties
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Mathematics (PM, volume 258)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Twisted Weyl Group Multiple Dirichlet Series: The Stable Case

    • Ben Brubaker, Daniel Bump, Solomon Friedberg
    Pages 1-26

  3. A Topological Model for Some Summand of the Eisenstein Cohomology of Congruence Subgroups

    • Jens Pranke
    Pages 27-85

  4. The Saito-Kurokawa Space of PGSp4 and Its Transfer to Inner Forms

    • Wee Teck Gan
    Pages 87-123

  5. Values of Archimedean Zeta Integrals for Unitary Groups

    • Paul Garrett
    Pages 125-148

  6. A Simple Proof of Rationality of Siegel-Weil Eisenstein Series

    • Michael Harris
    Pages 149-185

  7. Residues of Eisenstein Series and Related Problems

    • Dihua Jiang
    Pages 187-204

  8. Some Extensions of the Siegel-Weil Formula

    • Stephen S. Kudla
    Pages 205-237

  9. A Remark on Eisenstein Series

    • Erez M. Lapid
    Pages 239-249

  10. Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms

    • Kartik Prasanna
    Pages 251-269

  11. Functoriality and Special Values of L-Functions

    • A. Raghuram, Freydoon Shahidi
    Pages 271-293

  12. Bounds for Matrix Coefficients and Arithmetic Applications

    • Ramin Takloo-Bighash
    Pages 295-314
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Keywords

About this book

Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas that are not usually interacting with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series.

The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications that have arisen in several recent developments in arithmetic: Arakelov intersection theory on Shimura varieties, special values of L-functions and Iwasawa theory, and equidistribution of rational/integer points on homogeneous varieties. Key questions that are considered include: Is it possible to identify a class of Eisenstein series whose Fourier coefficients (resp. special values) encode significant arithmetic information? Do such series fit into p-adic families? Are the Eisenstein series that arise in counting problems of this type?

Editors and Affiliations

  • Department of Mathematics, University of California, San Diego, La Jolla, USA

    Wee Teck Gan

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Stephen S. Kudla

  • Courant Institute of Mathematical Sciences, New York University, New York, USA

    Yuri Tschinkel

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