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Table of contents

  1. Front Matter
  2. Rolf Sören Krausshar
    Pages 1-47
  3. Rolf Sören Krausshar
    Pages 117-149
  4. Back Matter

About this book

Introduction

This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces.

Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincaré series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced.

Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described.

Keywords

Clifford-Analysis Eisenstein-Reihen Modulformen Potentialtheorie Zahlentheorie spezielle Funktionen arithmetic calculus Hilbert space index theory number theory Potential theory Riemann zeta function zeta function

Authors and affiliations

  1. 1.Department of Mathematical AnalysisGhent UniversityGhentBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/b95203
  • Copyright Information Birkhäuser Basel 2004
  • Publisher Name Birkhäuser Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-7643-7059-6
  • Online ISBN 978-3-7643-7804-2
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site