Vector Valued Hecke Theory
In this thesis we study vector valued modular forms with respect to certain representations. We define Hecke operators and we prove a multiplicity one theorem. This works generally for representations with a kernel that contains some principal congruence subgroup. Afterwards, we focus on the Weil...
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2014
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| Online Access: | http://tuprints.ulb.tu-darmstadt.de/4238/1/phd.pdf Werner, Fabian <http://tuprints.ulb.tu-darmstadt.de/view/person/Werner=3AFabian=3A=3A.html> : Vector Valued Hecke Theory. Technische Universität, Darmstadt [Ph.D. Thesis], (2014) |
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ndltd-tu-darmstadt.de-oai-tuprints.ulb.tu-darmstadt.de-42382017-03-17T06:35:58Z http://tuprints.ulb.tu-darmstadt.de/4238/ Vector Valued Hecke Theory Werner, Fabian In this thesis we study vector valued modular forms with respect to certain representations. We define Hecke operators and we prove a multiplicity one theorem. This works generally for representations with a kernel that contains some principal congruence subgroup. Afterwards, we focus on the Weil representation. We study the effect of Hecke operators on vector valued Eisenstein series and theta series. Finally, we recall the concept of an isotropic oldform. We show that in certain cases, in fact, all forms are isotropic oldforms i.e. are induced by modular forms on smaller vector spaces. 2014-10-28 Ph.D. Thesis NonPeerReviewed text ger Creative Commons: Attribution-Share Alike 3.0 http://tuprints.ulb.tu-darmstadt.de/4238/1/phd.pdf Werner, Fabian <http://tuprints.ulb.tu-darmstadt.de/view/person/Werner=3AFabian=3A=3A.html> : Vector Valued Hecke Theory. Technische Universität, Darmstadt [Ph.D. Thesis], (2014) en info:eu-repo/semantics/doctoralThesis info:eu-repo/semantics/openAccess |
| collection |
NDLTD |
| language |
German en |
| format |
Others
|
| sources |
NDLTD |
| description |
In this thesis we study vector valued modular forms with respect to certain representations. We define Hecke operators and we prove a multiplicity one theorem. This works generally for representations with a kernel that contains some principal congruence subgroup.
Afterwards, we focus on the Weil representation. We study the
effect of Hecke operators on vector valued Eisenstein series and theta series. Finally, we recall the concept of an isotropic oldform. We show that in certain cases, in fact, all forms are isotropic oldforms i.e. are induced by modular forms on smaller vector spaces. |
| author |
Werner, Fabian |
| spellingShingle |
Werner, Fabian Vector Valued Hecke Theory |
| author_facet |
Werner, Fabian |
| author_sort |
Werner, Fabian |
| title |
Vector Valued Hecke Theory |
| title_short |
Vector Valued Hecke Theory |
| title_full |
Vector Valued Hecke Theory |
| title_fullStr |
Vector Valued Hecke Theory |
| title_full_unstemmed |
Vector Valued Hecke Theory |
| title_sort |
vector valued hecke theory |
| publishDate |
2014 |
| url |
http://tuprints.ulb.tu-darmstadt.de/4238/1/phd.pdf Werner, Fabian <http://tuprints.ulb.tu-darmstadt.de/view/person/Werner=3AFabian=3A=3A.html> : Vector Valued Hecke Theory. Technische Universität, Darmstadt [Ph.D. Thesis], (2014) |
| work_keys_str_mv |
AT wernerfabian vectorvaluedhecketheory |
| _version_ |
1718424065098645504 |