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.

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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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