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© 2002

Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors

  • Authors
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1780)

Table of contents

  1. Front Matter
    Pages N2-VIII
  2. Jan Hendrik Bruinier
    Pages 1-13
  3. Jan Hendrik Bruinier
    Pages 39-61
  4. Jan Hendrik Bruinier
    Pages 63-94
  5. Jan Hendrik Bruinier
    Pages 95-118
  6. Jan Hendrik Bruinier
    Pages 119-140
  7. Jan Hendrik Bruinier
    Pages 141-144
  8. Jan Hendrik Bruinier
    Pages 145-152
  9. Back Matter
    Pages 153-153

About this book

Introduction

Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.

Keywords

Automorphic form Chern class Heegner divisor Lattice Weil representation modular form orthogonal group

Bibliographic information

  • Book Title Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors
  • Authors Jan H. Bruinier
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI https://doi.org/10.1007/b83278
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-43320-0
  • eBook ISBN 978-3-540-45872-2
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VIII, 156
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Field Theory and Polynomials
    Algebraic Geometry
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