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Lecture Notes in Mathematics

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

Authors: Boylan, Hatice

  • 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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eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-319-12916-7
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  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-12915-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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)


Table of contents (4 chapters)

  • Finite Quadratic Modules

    Boylan, Hatice

    Pages 1-17

    Preview Buy Chapter 30,19 €
  • Weil Representations of Finite Quadratic Modules

    Boylan, Hatice

    Pages 19-64

    Preview Buy Chapter 30,19 €
  • Jacobi Forms over Totally Real Number Fields

    Boylan, Hatice

    Pages 65-101

    Preview Buy Chapter 30,19 €
  • Singular Jacobi Forms

    Boylan, Hatice

    Pages 103-122

    Preview Buy Chapter 30,19 €

Buy this book

eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-319-12916-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-12915-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields
Authors
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