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

Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors
Catalogue Information
Field name Details
Dewey Class 512.3
Title Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors ([EBook]) / by Jan H. Bruinier.
Author Bruinier, Jan Hendrik. , 1971-
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : Springer , 2002.
Physical Details VIII, 156 pages : online resource.
Series Lecture Notes in Mathematics 0075-8434 ; ; 1780
ISBN 9783540458722
Summary Note 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.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/b83278
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