Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change

  • Jayce Getz
  • Mark Goresky

Part of the Progress in Mathematics book series (PM, volume 298)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jayce Getz, Mark Goresky
    Pages 1-19
  3. Jayce Getz, Mark Goresky
    Pages 21-28
  4. Jayce Getz, Mark Goresky
    Pages 29-39
  5. Jayce Getz, Mark Goresky
    Pages 41-55
  6. Jayce Getz, Mark Goresky
    Pages 57-89
  7. Jayce Getz, Mark Goresky
    Pages 91-110
  8. Jayce Getz, Mark Goresky
    Pages 111-134
  9. Jayce Getz, Mark Goresky
    Pages 135-150
  10. Jayce Getz, Mark Goresky
    Pages 151-166
  11. Jayce Getz, Mark Goresky
    Pages 167-177
  12. Jayce Getz, Mark Goresky
    Pages 179-182
  13. Back Matter
    Pages 183-256

About this book

Introduction

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

Keywords

Fourier coefficients Hecke operators Hilbert modular varieties automorphic forms intersection cohomology

Authors and affiliations

  • Jayce Getz
    • 1
  • Mark Goresky
    • 2
  1. 1., Department of MathematicsMcGill UniversityMontrealCanada
  2. 2., School of MathematicsInstitute for Advanced StudyPrincetonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0351-9
  • Copyright Information Springer Basel 2012
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0350-2
  • Online ISBN 978-3-0348-0351-9
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book