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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
Links to Related Works	Subject References: Algebra . Algebraic Geometry . Field Theory and Polynomials . Field theory (Physics) . Mathematics . Authors: Bruinier, Jan Hendrik. 1971- . Bruinier, Jan Hendrik 1971- . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.3 .

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

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