ENGLISH

Generalized Analytic Automorphic Forms in Hypercomplex Spaces

By Rolf Sören Krausshar (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2004
ISBN
978-3-7643-7059-6, 978-3-7643-7804-2
DOI
10.1007/b95203
Language
english
Format
PDF
Filesize
1 MB (1144993 bytes)
Series
Frontiers in Mathematics
Edition
1
Pages
168\150
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Operational Calculus; Potential Theory; SequencesSeriesSpecial Functions; Integral TransformsSummability; Number Theory

Description

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.

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