Boylan, Hatice: Jacobi forms, finite quadratic modules and Weil representations over number fieldsJacobiformen, endliche quadratische Moduln und Weil-Darstellungen über Zahlkörpern. 2011
Inhalt
- Abstract
- Acknowledgments
- Contents
- Introduction
- Notations
- Chapter 1 - Finite Quadratic Modules
- 1.1 Finite quadratic O-modules
- 1.2 Cyclic finite quadratic O-modules
- 1.3 Some lemmas concerning quotients O=a
- Chapter 2 - Weil Representations of Finite Quadratic Modules
- 2.1 Review of representations of groups
- 2.2 The Weil representation W(M)
- 2.3 Decomposition of Weil representations
- 2.4 Complete decomposition of cyclic repre-sentations
- 2.5 The one dimensional subrepresentations
- 2.6 The number of irreducible components
- Chapter 3 - Jacobi Forms over Totally Real Number Fields
- 3.1 O-lattices
- 3.2 Algebraic prerequisites
- 3.3 The metaplectic cover ...
- 3.4 The Jacobi group of an O-lattice
- 3.5 The Jacobi theta functions
- 3.6 Basic properties of Jacobi forms
- 3.7 Jacobi forms as vector-valued Hilbertmodular forms
- 3.8 Appendix: Jacobi forms of odd index
- Chapter 4 - Singular Jacobi Forms
- 4.1 Characterization of singular Jacobi forms
- 4.2 Theta functions andWeil representations
- 4.3 Decomposition of the ...
- 4.4 The singular Jacobi forms of rank 1 index
- Chapter 5 - Tables
- Bibliography