Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Author:   Jan H. Bruinier
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   2002 ed.
Volume:   1780
ISBN:  

9783540433200


Pages:   156
Publication Date:   10 April 2002
Format:   Paperback
Availability:   In Print   Availability explained
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Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors


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 $(SL)_2$. 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.

Full Product Details

Author:   Jan H. Bruinier
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2002 ed.
Volume:   1780
Dimensions:   Width: 15.60cm , Height: 0.80cm , Length: 23.40cm
Weight:   0.530kg
ISBN:  

9783540433200


ISBN 10:   3540433201
Pages:   156
Publication Date:   10 April 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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 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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