Vector Valued Hecke Theory.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2014)
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|Item Type:||Ph.D. Thesis|
|Title:||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 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.
|Place of Publication:||Darmstadt|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 510 Mathematik|
|Divisions:||04 Department of Mathematics
04 Department of Mathematics > Algebra
|Date Deposited:||17 Nov 2014 07:48|
|Last Modified:||17 Nov 2014 14:23|
|Referees:||Scheithauer, Prof. Dr. Nils and Bruinier, Prof. Dr. Jan|
|Refereed:||16 October 2014|