Description
Book SynopsisModular forms and Jacobi forms play a central role in many areas of mathematics. In recent years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms.
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MAA ReviewsTable of Contents
- Background: Elliptic functions
- Theta functions and holomorphic Jacobi forms
- Classical Maass forms
- Harmonic Maass forms and mock modular forms: The basics
- Differential operators and mock modular forms
- Examples of harmonic Maass forms
- Hecke theory
- Zwegers' thesis
- Ramanujan's mock theta functions
- Holomorphic projection
- Meromorhic Jacobi forms
- Mock modular Eichler-shimura theory
- Related automorphic forms
- Applications: Partitions and unimodal sequences
- Asymptotics for coefficients of modular-type functions
- Harmonic Maass forms as arithmetic and geometric generating functions
- Shifted convolution $L$-functions
- Generalized Borcherds products
- Elliptic curves over $\mathbb{Q}$
- Representation theory and mock modular forms
- Quantum modular forms
- Representations of mock theta functions
- Bibliography
- Index
