Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors / Edition 1 by Jan H. Bruinier | 9783540433200 | Paperback | Barnes & Noble
Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors / Edition 1

Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors / Edition 1

by Jan H. Bruinier
     
 

ISBN-10: 3540433201

ISBN-13: 9783540433200

Pub. Date: 05/31/2002

Publisher: Springer Berlin Heidelberg

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

Overview

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.

Product Details

ISBN-13:
9783540433200
Publisher:
Springer Berlin Heidelberg
Publication date:
05/31/2002
Series:
Lecture Notes in Mathematics Series, #1780
Edition description:
2002
Pages:
156
Product dimensions:
9.21(w) x 6.14(h) x 0.35(d)

Table of Contents

Introduction.- Vector valued modular forms for the metaplectic group. The Weil representation. Poincaré series and Einstein series. Non-holomorphic Poincaré 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 Lsubp-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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