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

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 $(SL)_2(R)$. T...

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Bibliographic Details
Main Author: Bruinier, Jan H. (Jan Hendrik), 1971-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer-Verlag, [2002]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1780.
Subjects:
Forms, Modular.
Series, Theta.
Picard groups.
Algebraic cycles.
Chern classes.
Algebraischer Zyklus.
Automorphe Form.
Modulform.
Divisor.
Formes modulaires.
Cycles algébriques.
Fonctions thêta.
Chern, Classes de.
Electronic books.
Online Access:Connect to the full text of this electronic book
Description
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.
Item Description:Electronic resource.
Physical Description:1 online resource (viii, 152 pages)
Bibliography:Includes bibliographical references and index.
ISBN:9783540458722 (electronic bk.)
3540458727 (electronic bk.)
ISSN:0075-8434 ;