Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the n-Dimensional Hyperbolic Space

Details Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the n-Dimensional Hyperbolic Space Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the n-Dimensional Hyperbolic Space

2004-01-16

arxiv.org/abs/math/0401197v1

Mathematics

Number Theory

18 pages

Scientific paper

This paper deals with a new analytic type of vector- and Clifford algebra valued automorphic forms in one and two vector variables. For hypercomplex generalizations of the classical modular group and their arithmetic congruence subgroups Eisenstein- and Poincar\'e type series that are annihilated by Dirac operators, and more generally, by iterated Dirac operators on the upper half-space of $R^n$ are discussed. In particular we introduce (poly-)monogenic modular forms on hypercomplex generalizations of the classical theta group.

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