Generalized Analytic Automorphic Forms in Hypercomplex Spaces (Frontiers in Mathematics)
Edition: 1 edition
Publisher: Birkhauser
Published: May 27, 2004
Language: eng
Format: Paperback
Number of pages: 167
ISBN-13: 9783764370596
Subjects: Complex analysis; Number Theory; Mathematics; Science/Mathematics; Calculus; Mathematical Analysis; Clifford-Analysis; Eisenstein-Reihen; Mathematics / Mathematical Analysis; Modulformen; Potentialtheorie; Zahlentheorie; spezielle Funktionen
First sentence: Hypercomplex numbers are, roughly speaking, generalizations of the complex numbers in the sense of having several imaginary units.
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.