Dittmann, Moritz Christopher (2018)
Reflective Automorphic Forms and Siegel Theta Series for Niemeier Lattices.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung
Kurzbeschreibung (Abstract)
The first part of this thesis is about reflective automorphic forms on lattices of squarefree level that split two hyperbolic planes. We show that there are only finitely many possibilities for this lattice and give a complete classification of strongly-reflective automorphic forms of singular weight for the discriminant kernel of such a lattice.
In the second part we use Siegel theta series for Niemeier lattices to construct a basis of the space of Siegel cusp forms of degree 6 and weight 14. We use this to show that the Kodaira dimension of the moduli space of principally polarized abelian varieties of dimension 6 is non-negative.
| Typ des Eintrags: | Dissertation | ||||
|---|---|---|---|---|---|
| Erschienen: | 2018 | ||||
| Autor(en): | Dittmann, Moritz Christopher | ||||
| Art des Eintrags: | Erstveröffentlichung | ||||
| Titel: | Reflective Automorphic Forms and Siegel Theta Series for Niemeier Lattices | ||||
| Sprache: | Englisch | ||||
| Referenten: | Scheithauer, Prof. Dr. Nils ; Möller, Prof. Dr. Martin ; Salvati Manni, Prof. Dr. Riccardo | ||||
| Publikationsjahr: | 2018 | ||||
| Ort: | Darmstadt | ||||
| Datum der mündlichen Prüfung: | 6 September 2018 | ||||
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/8115 | ||||
| Kurzbeschreibung (Abstract): | The first part of this thesis is about reflective automorphic forms on lattices of squarefree level that split two hyperbolic planes. We show that there are only finitely many possibilities for this lattice and give a complete classification of strongly-reflective automorphic forms of singular weight for the discriminant kernel of such a lattice. In the second part we use Siegel theta series for Niemeier lattices to construct a basis of the space of Siegel cusp forms of degree 6 and weight 14. We use this to show that the Kodaira dimension of the moduli space of principally polarized abelian varieties of dimension 6 is non-negative. |
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| Alternatives oder übersetztes Abstract: |
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| URN: | urn:nbn:de:tuda-tuprints-81157 | ||||
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Algebra 04 Fachbereich Mathematik > Algebra > Unendlichdimensionale Lie-Algebren, Vertexalgebren, Automorphe Formen |
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| Hinterlegungsdatum: | 11 Nov 2018 20:55 | ||||
| Letzte Änderung: | 11 Nov 2018 20:55 | ||||
| PPN: | |||||
| Referenten: | Scheithauer, Prof. Dr. Nils ; Möller, Prof. Dr. Martin ; Salvati Manni, Prof. Dr. Riccardo | ||||
| Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 6 September 2018 | ||||
| Export: | |||||
| Suche nach Titel in: | TUfind oder in Google | ||||
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