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- catalog abstract "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.".
- catalog contributor b13302704.
- catalog created "c2004.".
- catalog date "2004".
- catalog date "c2004.".
- catalog dateCopyrighted "c2004.".
- catalog description "Includes bibliographical references (p. [151]-161) and index.".
- catalog description "Introduction -- 1. Function Theory in Hypercomplex Spaces -- 2. Clifford-analytic Eisenstein Series Associated to Translation Groups -- 3. Clifford-analytic Modular Forms -- Bibliography -- Index.".
- catalog 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.".
- catalog extent "xv, 167 p. ;".
- catalog identifier "0817670599 (acid-free paper)".
- catalog identifier "3764370599 (acid-free paper)".
- catalog isPartOf "Frontiers in mathematics".
- catalog issued "2004".
- catalog issued "c2004.".
- catalog language "eng".
- catalog publisher "Basel ; Boston : Birkhäuser Verlag,".
- catalog subject "515/.9 22".
- catalog subject "Automorphic forms.".
- catalog subject "Functions of complex variables.".
- catalog subject "Functions, special.".
- catalog subject "Hardy spaces.".
- catalog subject "Integral Transforms.".
- catalog subject "Mathematics.".
- catalog subject "Number theory.".
- catalog subject "Potential theory (Mathematics).".
- catalog subject "QA353.A9 K73 2004".
- catalog subject "Sequences (Mathematics).".
- catalog tableOfContents "Introduction -- 1. Function Theory in Hypercomplex Spaces -- 2. Clifford-analytic Eisenstein Series Associated to Translation Groups -- 3. Clifford-analytic Modular Forms -- Bibliography -- Index.".
- catalog title "Generalized analytic automorphic forms in hypercomplex spaces / Rolf Sören Krausshar.".
- catalog type "text".