책 이미지
eBook 미리보기
책 정보
· 제목 : Harmonic Maass Forms and Mock Modular Forms (Hardcover) (Theory and Applications)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470419448
· 쪽수 : 391쪽
· 출판일 : 2018-01-08
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470419448
· 쪽수 : 391쪽
· 출판일 : 2018-01-08
목차
- 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
