Lecture Notes in Mathematics

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

Authors: Bruinier, Jan H.

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About this book

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.

Table of contents (8 chapters)

  • Introduction

    Bruinier, Jan Hendrik

    Pages 1-13

  • 1. Vector valued modular forms for the metaplectic group

    Bruinier, Jan Hendrik

    Pages 15-38

  • 2. The regularized theta lift

    Bruinier, Jan Hendrik

    Pages 39-61

  • 3. The Fourier expansion of the theta lift

    Bruinier, Jan Hendrik

    Pages 63-94

  • 4. Some Riemann geometry on O(2,l)

    Bruinier, Jan Hendrik

    Pages 95-118

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-45872-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-43320-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1780
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45872-2
DOI
10.1007/b83278
Softcover ISBN
978-3-540-43320-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 156
Topics