CM values of regularized theta lifts
In this thesis, special values of regularized theta lifts at complex multiplication (CM) points are studied. In particular, it is shown that CM values of Borcherds products can be expressed in terms of finitely many Fourier coefficients of certain harmonic weak Maass forms of weight one. As it turns...
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2013
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| Online Access: | http://tuprints.ulb.tu-darmstadt.de/3731/1/main.pdf Ehlen, Stephan Jakob <http://tuprints.ulb.tu-darmstadt.de/view/person/Ehlen=3AStephan_Jakob=3A=3A.html> : CM values of regularized theta lifts. Technische Universität, Darmstadt [Ph.D. Thesis], (2013) |
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ndltd-tu-darmstadt.de-oai-tuprints.ulb.tu-darmstadt.de-37312017-03-17T06:35:49Z http://tuprints.ulb.tu-darmstadt.de/3731/ CM values of regularized theta lifts Ehlen, Stephan Jakob In this thesis, special values of regularized theta lifts at complex multiplication (CM) points are studied. In particular, it is shown that CM values of Borcherds products can be expressed in terms of finitely many Fourier coefficients of certain harmonic weak Maass forms of weight one. As it turns out, these coefficients are logarithms of algebraic integers whose prime ideal factorization is determined by cycles on an arithmetic curve that parametrize special endomorphisms of CM elliptic curves. 2013 Ph.D. Thesis NonPeerReviewed text ger Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0 http://tuprints.ulb.tu-darmstadt.de/3731/1/main.pdf Ehlen, Stephan Jakob <http://tuprints.ulb.tu-darmstadt.de/view/person/Ehlen=3AStephan_Jakob=3A=3A.html> : CM values of regularized theta lifts. Technische Universität, Darmstadt [Ph.D. Thesis], (2013) en info:eu-repo/semantics/doctoralThesis info:eu-repo/semantics/openAccess |
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NDLTD |
| language |
German en |
| format |
Others
|
| sources |
NDLTD |
| description |
In this thesis, special values of regularized theta lifts at complex multiplication (CM) points are studied. In particular, it is shown that CM values of Borcherds products can be expressed in terms of finitely many Fourier coefficients of certain harmonic weak Maass forms of weight one. As it turns out, these coefficients are logarithms of algebraic integers whose prime ideal factorization is determined by cycles on an arithmetic curve that parametrize special endomorphisms of CM elliptic curves. |
| author |
Ehlen, Stephan Jakob |
| spellingShingle |
Ehlen, Stephan Jakob CM values of regularized theta lifts |
| author_facet |
Ehlen, Stephan Jakob |
| author_sort |
Ehlen, Stephan Jakob |
| title |
CM values of regularized theta lifts |
| title_short |
CM values of regularized theta lifts |
| title_full |
CM values of regularized theta lifts |
| title_fullStr |
CM values of regularized theta lifts |
| title_full_unstemmed |
CM values of regularized theta lifts |
| title_sort |
cm values of regularized theta lifts |
| publishDate |
2013 |
| url |
http://tuprints.ulb.tu-darmstadt.de/3731/1/main.pdf Ehlen, Stephan Jakob <http://tuprints.ulb.tu-darmstadt.de/view/person/Ehlen=3AStephan_Jakob=3A=3A.html> : CM values of regularized theta lifts. Technische Universität, Darmstadt [Ph.D. Thesis], (2013) |
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AT ehlenstephanjakob cmvaluesofregularizedthetalifts |
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