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＜E-Book＞
Generalized Analytic Automorphic Forms in Hypercomplex Spaces / by Rolf S. Krausshar
(Frontiers in Mathematics. ISSN:16608054)

Edition	1st ed. 2004.
Publisher	Basel : Birkhäuser Basel : Imprint: Birkhäuser
Year	2004
Language	English
Size	XV, 168 p : online resource
Authors	*Krausshar, Rolf S author SpringerLink (Online service)
Subjects	LCSH:Special functions LCSH:Mathematical analysis LCSH:Potential theory (Mathematics) LCSH:Sequences (Mathematics) LCSH:Number theory FREE:Special Functions FREE:Integral Transforms and Operational Calculus FREE:Potential Theory FREE:Sequences, Series, Summability FREE:Number Theory
Notes	Introduction -- 1. Function Theory in Hypercomplex Spaces -- 2. Clifford-analytic Eisenstein Series Associated to Translation Groups -- 3. Clifford-analytic Modular Forms -- Bibliography -- Index 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 HTTP:URL=https://doi.org/10.1007/b95203

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