000 | 03151nam a22004815i 4500 | ||
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001 | 978-3-540-45872-2 | ||
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008 | 121227s2002 gw | s |||| 0|eng d | ||
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_a9783540458722 _9978-3-540-45872-2 |
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024 | 7 |
_a10.1007/b83278 _2doi |
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_aPBF _2bicssc |
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_aMAT002010 _2bisacsh |
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_aPBF _2thema |
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_a512.3 _223 |
100 | 1 |
_aBruinier, Jan H. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aVIII, 156 p. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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_aLecture Notes in Mathematics, _x0075-8434 ; _v1780 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b83278 |
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912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
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_c11421 _d11421 |