Generalized analytic automorphic forms in hypercomplex spaces超复空间的广义解析自守形成
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作者： Rolf S. Krausshar著
出 版 社：
出版时间： 2004-5-1字数：版次： 1页数： 167印刷时间： 2004/05/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783764370596包装： 平装内容简介
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.
目录
Introduction
1 Function theory in hypercomplex spaces
1.1 Hypercomplex numbers and Clifford Algebras . .
1.2 Vahlen groups and arithmetic subgroups
1.3 Differentiability, conformality and analyticity in hypercomplex spaces
1.4 Basic theorems of Clifford analysis
1.5 Orders of isolated a-points, an argument principleand Rouchd's theorem
1.6 The generalized negative power functions
2 Clifford-analytic Eisenstein series associated to translation groups
2.1 Multiperiodic Mittag-Leffter series
2.2 Some results on the zeroes of the generalized cotangent and tangent
2.3 Liouville type theorems for generalized elliptic functions
2.4 Series expansions, divisor sums and Dirichlet series
2.5 The integer multiplication of the Clifford-analytic Eisenstein series
2.6 Characterization theorems
2.7 Lattices with hypercompiex multiplication
2.8 Bergman kernels of rectangular domains
2.9 Szeg5 kernels of strip domains
2.10 Boundary value problems on conformally flat cylinders and tori . .
2.11 Order theory and argument principles on cylinders and tori3
3Clifford-analytic Modular Forms
3.1 Rotation and translation invariant Eisenstein series
3.2 Clifford-analytic modular forms in one hypercomplex variable . .
3.3 Clifford-analytic modular forms in two and several hypercomplex variables
3.4Some remarks on clifford-analytic modular forms in real and complex minkowski spaces
3.5 Some perspectives
Bibliography
List of symbols
Index
