| 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 principle and 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 3 Clifford-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 3.4 Some remarks on clifford-analytic modular forms in real and complex minkowski spaces 3.5 Some perspectives Bibliography List of symbols Index |
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