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＜電子ブック＞
Generalized Analytic Automorphic Forms in Hypercomplex Spaces / by Rolf S. Krausshar
(Frontiers in Mathematics. ISSN:16608054)

版	1st ed. 2004.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2004
本文言語	英語
大きさ	XV, 168 p : online resource
著者標目	*Krausshar, Rolf S author SpringerLink (Online service)
件　名	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
一般注記	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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