Jan H. Bruinier
Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Paperback Engels 2002 2002e druk 9783540433200
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Samenvatting
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.
Specificaties
ISBN13:9783540433200
Taal:Engels
Bindwijze:paperback
Aantal pagina's:156
Uitgever:Springer Berlin Heidelberg
Druk:2002
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Inhoudsopgave
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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