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Groups Acting on Hyperbolic Space

Harmonic Analysis and Number Theory

  • Jürgen Elstrodt
  • Fritz Grunewald
  • Jens Mennicke
Book

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 1-32
  3. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 33-81
  4. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 83-129
  5. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 131-183
  6. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 185-229
  7. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 231-310
  8. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 311-357
  9. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 359-405
  10. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 407-441
  11. Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 443-495
  12. Back Matter
    Pages 497-524

About this book

Introduction

This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva­ ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n :::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres. The ge­ ometries underlying the hyperbolic spaces were of fundamental importance since Lobachevski, Bolyai and Gauß had observed that they do not satisfy the axiom of parallels. Already in the classical works several concrete coordinate models of hy­ perbolic 3-space have appeared. They make explicit computations possible and also give identifications of the full group of motions or isometries with well-known matrix groups. One such model, due to H. Poincare, is the upper 3 half-space IH in JR . The group of isometries is then identified with an exten­ sion of index 2 of the group PSL(2,

Keywords

calculus discontinuous group eisenstein series harmonic analysis hermitian form hyperbolic space number theory trace formula

Authors and affiliations

  • Jürgen Elstrodt
    • 1
  • Fritz Grunewald
    • 2
  • Jens Mennicke
    • 3
  1. 1.Mathematisches InstitutUniversität MünsterMünsterGermany
  2. 2.Mathematisches InstitutUniversität DüsseldorfDüsseldorfGermany
  3. 3.Fakultät für MathematikUniversität BielefeldBielefeldGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03626-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08302-0
  • Online ISBN 978-3-662-03626-6
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site