Ajouz, Ali: Hecke operators on Jacobi forms of lattice index and the relation to elliptic modular formsHecke-Operatoren für Jacobiformen mit Gitterindex und die Beziehung zu elliptischen Modulformen. 2015
Content
- Abstract
- Table of Contents
- Introduction and Statement of Results
- Preliminaries
- Hecke Theory of Jacobi Forms of Lattice Index
- Some Lemmas on Lattices and Gauss Sums
- Jacobi Groups of Integral Lattice
- Theta Series
- Jacobi Forms of Lattice Index
- Hecke Operators on the Space of Jacobi Forms
- The Action of Hecke Operators on Fourier Coefficients
- Hecke Operators and Euler Products
- Basis of Simultaneous Eigenforms
- The Action of the Orthogonal Group
- Jacobi Cusp Forms and Hecke Operators
- Jacobi-Eisenstein Series and Hecke Operators
- Lifting to Elliptic Modular Forms
- Lifting via Shimura Correspondence for Half Integral Weight
- Lifting via Stable Isomorphisms between Lattices
- Lifting from Elliptic Modular Forms
- Appendix
- List of Notations
- Bibliography