Generalized Analytic Automorphic Forms in Hypercomplex Spaces
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Beschreibung
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.
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
This book provides a comprehensive overview of the basic theory of hypercomplex-analytic automorphic forms and functions in higher dimensional spaces. It gives a summary on the research results obtained over the last five years and establishes a new field within the theory of functions of hypercomplex variables and within analytic number theory.
Autor*in
Rolf S. Krausshar
Themen in »Generalized Analytic Automorphic Forms in Hypercomplex Spaces«
Clifford-Analysis Eisenstein-Reihen Modulformen Potentialtheorie Zahlentheorie spezielle Funktionen arithmetic calculus Hilbert space index theory number theory Potential theory Riemann zeta function zeta function
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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)
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