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

  • Authors
  • Jan¬†H.¬†Bruinier

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

  • DOI https://doi.org/10.1007/b83278
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43320-0
  • Online ISBN 978-3-540-45872-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site