Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields
Authors: Boylan, Hatice
Free Preview- Presents a theory which is intended to open new directions of research in the theory of Hilbert modular forms
- Provides a steep introduction to Weil representations of Hilbert modular groups
- Provides the basic tools for a comprehensive theory of Jacobi forms over number fields
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- About this book
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The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory of Jacobi forms over the rational numbers, which is an indispensable tool in the arithmetic theory of elliptic modular forms, elliptic curves, and in many other disciplines in mathematics and physics. Jacobi forms can be viewed as vector valued modular forms which take values in so-called Weil representations. Accordingly, the first two chapters develop the theory of finite quadratic modules and associated Weil representations over number fields. This part might also be interesting for those who are merely interested in the representation theory of Hilbert modular groups. One of the main applications is the complete classification of Jacobi forms of singular weight over an arbitrary totally real number field.
- Reviews
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“The classical theory of Jacobi forms, and its connections to elliptic modular forms, have been a constant subject of research for many decades. … this book is valuable contribution to the mathematical society, and serves as a welcoming invitation to anyone who finds interest in engaging him/herself in researching this beautiful new theory.” (Shaul Zemel, zbMATH 1317.11002, 2015)
- Table of contents (4 chapters)
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Finite Quadratic Modules
Pages 1-17
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Weil Representations of Finite Quadratic Modules
Pages 19-64
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Jacobi Forms over Totally Real Number Fields
Pages 65-101
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Singular Jacobi Forms
Pages 103-122
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Table of contents (4 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields
- Authors
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- Hatice Boylan
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 2130
- Copyright
- 2015
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-12916-7
- DOI
- 10.1007/978-3-319-12916-7
- Softcover ISBN
- 978-3-319-12915-0
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- XIX, 130
- Topics
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