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A Theory of Modular Forms in Clifford Analysis, their Applications and Perspectives

  • Rolf Sören Kraußhar
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

This chapter is devoted to monogenic, harmonic and polymono-genic Clifford-valued automorphic forms that are related to discrete subgroups of Vahlen groups acting on half-spaces of real and complex Minkowski type spaces. In particular, Eisenstein and Poincaré type series are constructed within this framework.

We discuss their basic properties and provide a short overview about their range of applications to several areas from pure and applied mathematics, as for example, to number theory, to functional analysis and to order theory and pde’s on manifolds.

Keywords

Clifford analysis automorphic forms Vahlen groups Minkowski type-spaces function spaces partial differential equations order theory argument principles on conformal manifolds 

Mathematics Subject Classification (2000)

11F03 11F55 30G35 11G15 

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Rolf Sören Kraußhar
    • 1
  1. 1.Vakgroep Wiskundige AnalyseUniversiteit GentGentBelgium

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