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Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103540433201
ISBN-139783540433200
eBay Product ID (ePID)2289070
Product Key Features
Number of PagesVIII, 156 Pages
LanguageEnglish
Publication NameBorcherds Products Ono (2 ,L) and Chern Classes of Heegner Divisors
SubjectAlgebra / Abstract, Functional Analysis, Geometry / Algebraic
Publication Year2002
TypeTextbook
AuthorJan H. Bruinier
Subject AreaMathematics
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight18.7 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2002-023605
Series Volume Number1780
Number of Volumes1 vol.
IllustratedYes
Table Of ContentIntroduction.- 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.
SynopsisAround 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., 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, 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.
LC Classification NumberQA247-247.45
