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.…mehr
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.
Artikelnr. des Verlages: 10866610, 978-3-540-43320-0
2002
Seitenzahl: 164
Erscheinungstermin: 10. April 2002
Englisch
Abmessung: 235mm x 155mm x 10mm
Gewicht: 251g
ISBN-13: 9783540433200
ISBN-10: 3540433201
Artikelnr.: 10613766
Herstellerkennzeichnung
Die Herstellerinformationen sind derzeit nicht verfügbar.
Autorenporträt
Jan H. Bruinier, University of Heidelberg, Germany
Inhaltsangabe
From the contents: - Introduction - Vector valued modular forms for the metaplectic group. The Weil representation. Poincare series and Einstein series. Non-holomorphic Poincare 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 Lapestimates. 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.
From the contents: - Introduction - Vector valued modular forms for the metaplectic group. The Weil representation. Poincare series and Einstein series. Non-holomorphic Poincare 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 Lapestimates. 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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