## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Rolf Sören Kraußhar

#### Abstract

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 Poincaré type series that are annihilated by Dirac operators, and more generally, by iterated Dirac operators on the upper half-space of $\mathbb{R}^n$ are discussed. In particular we introduce (poly-)monogenic modular forms on hypercomplex generalizations of the classical theta group.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 11, Number 5 (2005), 759-774.

Dates
First available in Project Euclid: 7 March 2005

https://projecteuclid.org/euclid.bbms/1110205631

Mathematical Reviews number (MathSciNet)
MR2130637

Zentralblatt MATH identifier
1064.11033

Subjects
Primary: 11 F 03 30 G 35 11 F 55

#### Citation

Kraußhar, Rolf Sören. Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the $n$-Dimensional Hyperbolic Space. Bull. Belg. Math. Soc. Simon Stevin 11 (2005), no. 5, 759--774.https://projecteuclid.org/euclid.bbms/1110205631