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001 978-3-540-45872-2
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008 121227s2002 gw | s |||| 0|eng d
020 _a9783540458722
_9978-3-540-45872-2
024 7 _a10.1007/b83278
_2doi
050 4 _aQA247-QA247.45
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.3
_223
100 1 _aBruinier, Jan H.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBorcherds Products on O(2, l) and Chern Classes of Heegner Divisors
_h[electronic resource] /
_cby Jan H. Bruinier.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aVIII, 156 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1780
505 0 _aIntroduction -- 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.
520 _aAround 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.
650 0 _aField theory (Physics).
650 0 _aGeometry, algebraic.
650 1 4 _aField Theory and Polynomials.
_0http://scigraph.springernature.com/things/product-market-codes/M11051
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540433200
776 0 8 _iPrinted edition:
_z9783662163696
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1780
856 4 0 _uhttps://doi.org/10.1007/b83278
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11421
_d11421