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

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  • © 2002

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Authors:
  1. Jan H. Bruinier
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1780)

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Table of contents (8 chapters)

  1. Front Matter

    Pages N2-VIII
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  2. Introduction

    • Jan Hendrik Bruinier
    Pages 1-13

  3. 1. Vector valued modular forms for the metaplectic group

    • Jan Hendrik Bruinier
    Pages 15-38

  4. 2. The regularized theta lift

    • Jan Hendrik Bruinier
    Pages 39-61

  5. 3. The Fourier expansion of the theta lift

    • Jan Hendrik Bruinier
    Pages 63-94

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

    • Jan Hendrik Bruinier
    Pages 95-118

  7. 5. Chern classes of Heegner divisors

    • Jan Hendrik Bruinier
    Pages 119-140

  8. References

    • Jan Hendrik Bruinier
    Pages 141-144

  9. Subject Index and Notation Index

    • Jan Hendrik Bruinier
    Pages 145-152

  10. Back Matter

    Pages 153-153
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Keywords

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.

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

  • DOI: https://doi.org/10.1007/b83278

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43320-0Published: 10 April 2002

  • eBook ISBN: 978-3-540-45872-2Published: 11 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 156

  • Topics: Field Theory and Polynomials, Algebraic Geometry

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