Borcherds products on O(2, l) and Chern classes of Heegner divisors /

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Bibliographic Details
Author / Creator:	Bruinier, Jan H. (Jan Hendrik), 1971-
Imprint:	Berlin ; New York : Springer-Verlag, ©2002.
Description:	1 online resource (viii, 152 pages).
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1780 Lecture notes in mathematics (Springer-Verlag) ; 1780.
Subject:	Forms, Modular. Series, Theta. Picard groups. Algebraic cycles. Chern classes. Algebraic cycles. Chern classes. Forms, Modular. Picard groups. Series, Theta.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11064916

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ISBN:	9783540458722 3540458727 9783540433200 3540433201
Notes:	Includes bibliographical references and index. Print version record.
Summary:	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.
Other form:	Print version: Bruinier, Jan H. (Jan Hendrik), 1971- Borcherds products on 0(2,1) and Chern classes of Heegner divisors. Berlin ; New York : Springer-Verlag, ©2002 3540433201

Table of Contents:

Introduction
Vector valued modular forms for the metaplectic group. The Weil representation. Poincar series and Einstein series. Non-holomorphic Poincar series of negative weight
The regularized theta lift. Siegel theta functions. The theta integral. Unfolding against F. Unfolding against theta
The Fourier theta lift. Lorentzian lattices. Lattices of signature (2,l). Modular forms on orthogonal groups. Borcherds products
Some Riemann geometry on O(2,l). The invariant Laplacian. Reduction theory and L^p-estimates. Modular forms with zeros and poles on Heegner divisors
Chern classes of Heegner divisors. A lifting into cohomology. Modular forms with zeros and poles on Heegner divisors II.

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