Jan H. Bruinier
Springer Berlin Heidelberg
2002e druk, 2002
9783540433200
Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Specificaties
Paperback, 156 blz.
|
Engels
Springer Berlin Heidelberg |
2002e druk, 2002
ISBN13: 9783540433200
Rubricering
Juridisch
:
Onderdeel van serie
Lecture Notes in Mathematics
Verwachte levertijd ongeveer 9 werkdagen
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
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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