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Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields

  • Book
  • © 2015

Overview

Authors:
  1. Hatice Boylan

    1. Matematik Bölümü, İstanbul Üniversitesi, İstanbul, Turkey

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  • 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

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2130)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xix
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  2. Finite Quadratic Modules

    • Hatice Boylan
    Pages 1-17

  3. Weil Representations of Finite Quadratic Modules

    • Hatice Boylan
    Pages 19-64

  4. Jacobi Forms over Totally Real Number Fields

    • Hatice Boylan
    Pages 65-101

  5. Singular Jacobi Forms

    • Hatice Boylan
    Pages 103-122

  6. Back Matter

    Pages 123-132
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Keywords

About this book

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

“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)

Authors and Affiliations

  • Matematik Bölümü, İstanbul Üniversitesi, İstanbul, Turkey

    Hatice Boylan

Bibliographic Information

  • Book Title: Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields

  • Authors: Hatice Boylan

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-12916-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Softcover ISBN: 978-3-319-12915-0Published: 16 December 2014

  • eBook ISBN: 978-3-319-12916-7Published: 05 December 2014

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIX, 130

  • Topics: Number Theory

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