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

  • Hatice Boylan

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

  • Hatice Boylan
    • 1
  1. 1.Matematik Bölümüİstanbul ÜniversitesiİstanbulTurkey

Bibliographic information

  • 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
  • Print ISBN 978-3-319-12915-0
  • Online ISBN 978-3-319-12916-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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