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Modern Birkhäuser Classics

Elements of the Representation Theory of the Jacobi Group

Authors: Berndt, Rolf, Schmidt, Ralf

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  • Very well written monograph combining algebraic groups and number theory
  • Recommended reading for researchers of modular and automorphic forms
  • Up to date and structured collection of known results
see more benefits

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-0348-0283-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-3-0348-0282-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve.

This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier.

Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.

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The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field.

(Zentralblatt MATH)

 

This book is certainly recommended for researchers interested in modular and automorphic forms.

(Mathematical Reviews)

 

This book complements the book on Jacobi forms by M. Eichler and D. Zagier and includes many of the author's original results. It can be read, however, independently of other sources, and it will be very useful for researchers interested in algebraic groups and number theory.

(Mathematica)

About the authors

Rolf Berndt is a Professor of Mathematics at the University of Hamburg.

Ralf Schmidt is a Professor of Mathematics at the University of Oklahoma, Norman, OK, USA.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-0348-0283-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-3-0348-0282-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Elements of the Representation Theory of the Jacobi Group
Authors
Series Title
Modern Birkhäuser Classics
Copyright
1998
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-0283-3
DOI
10.1007/978-3-0348-0283-3
Softcover ISBN
978-3-0348-0282-6
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XIII, 213
Topics