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

  • 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

Book

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

Table of contents

  1. Front Matter
    Pages i-xix
  2. Hatice Boylan
    Pages 1-17
  3. Hatice Boylan
    Pages 103-122
  4. Back Matter
    Pages 123-132

About this book

Introduction

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.

Keywords

11F50,11F27 Automorhic forms of singular weight Finite quadratic modules Jacobi Forms Weil representations

Authors and affiliations

  1. 1.Matematik Bölümüİstanbul ÜniversitesiİstanbulTurkey

Bibliographic information

  • Book Title Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields
  • Authors Hatice Boylan
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • DOI https://doi.org/10.1007/978-3-319-12916-7
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-12915-0
  • eBook ISBN 978-3-319-12916-7
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XIX, 130
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
  • Buy this book on publisher's site
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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)