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

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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

Permanent link to this document
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

Keywords
automorphic forms arithmetic subgroups of the orthogonal group functions of hypercomplex variables Dirac operators Clifford algebras

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.


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