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Record Nr. |
UNINA9910144943803321 |
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Autore |
Bruinier Jan H |
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Titolo |
Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors / / by Jan H. Bruinier |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 |
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ISBN |
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Edizione |
[1st ed. 2002.] |
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Descrizione fisica |
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1 online resource (VIII, 156 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1780 |
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Disciplina |
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Soggetti |
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Algebra |
Field theory (Physics) |
Algebraic geometry |
Field Theory and Polynomials |
Algebraic Geometry |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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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Sommario/riassunto |
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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 |
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