Ehlen, Stephan Jakob (2013)
CM values of regularized theta lifts.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung
Kurzbeschreibung (Abstract)
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.
Typ des Eintrags: | Dissertation | ||||
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Erschienen: | 2013 | ||||
Autor(en): | Ehlen, Stephan Jakob | ||||
Art des Eintrags: | Erstveröffentlichung | ||||
Titel: | CM values of regularized theta lifts | ||||
Sprache: | Englisch | ||||
Referenten: | Bruinier, Prof. Dr. Jan Hendrik ; Scheithauer, Prof Dr. Nils ; Yang, Prof. Tonghai | ||||
Publikationsjahr: | 2013 | ||||
Ort: | Darmstadt | ||||
Datum der mündlichen Prüfung: | 20 September 2013 | ||||
URL / URN: | http://tuprints.ulb.tu-darmstadt.de/3731 | ||||
Kurzbeschreibung (Abstract): | 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. |
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Alternatives oder übersetztes Abstract: |
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Freie Schlagworte: | CM values, regularized theta lifts, Borcherds products, harmonic weak Maass forms, Kudla program | ||||
URN: | urn:nbn:de:tuda-tuprints-37314 | ||||
Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik > Algebra 04 Fachbereich Mathematik |
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Hinterlegungsdatum: | 22 Dez 2013 20:55 | ||||
Letzte Änderung: | 22 Dez 2013 20:55 | ||||
PPN: | |||||
Referenten: | Bruinier, Prof. Dr. Jan Hendrik ; Scheithauer, Prof Dr. Nils ; Yang, Prof. Tonghai | ||||
Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 20 September 2013 | ||||
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