Overview
- First extensive, comprehensive detailed and rather offrounded treatment of the basic theory of hypercomplex-analytic automorphic forms
- Summarizes recent research results on a new branch within hypercomplex analysis and analytic number theory
- Provides a breakthru in this research field and opens the door for further investigation in this line
- Includes useful perspectives for applications to function spaces and global analysis, as it develops new methods to tackle these problems
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (3 chapters)
Keywords
About this book
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.
Reviews
From the reviews:
“Its remarkable feature is a masterful combination of deep and sophisticated results with very accessible form of presentation. I am sure the book will have numerous and far-reaching consequences and repercussions.”(ZENTRALBLATT MATH)
Authors and Affiliations
Bibliographic Information
Book Title: Generalized Analytic Automorphic Forms in Hypercomplex Spaces
Authors: Rolf Sören Krausshar
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/b95203
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Birkhäuser Basel 2004
Softcover ISBN: 978-3-7643-7059-6Published: 23 February 2004
eBook ISBN: 978-3-7643-7804-2Published: 02 February 2005
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XV, 168
Topics: Special Functions, Integral Transforms, Operational Calculus, Potential Theory, Sequences, Series, Summability, Number Theory