Open Access
Translator Disclaimer
March 2005 Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the $n$-Dimensional Hyperbolic Space
Rolf Sören Kraußhar
Bull. Belg. Math. Soc. Simon Stevin 11(5): 759-774 (March 2005). DOI: 10.36045/bbms/1110205631

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.

Citation

Download Citation

Rolf Sören Kraußhar. "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 (5) 759 - 774, March 2005. https://doi.org/10.36045/bbms/1110205631

Information

Published: March 2005
First available in Project Euclid: 7 March 2005

zbMATH: 1064.11033
MathSciNet: MR2130637
Digital Object Identifier: 10.36045/bbms/1110205631

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

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

Rights: Copyright © 2005 The Belgian Mathematical Society

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.11 • No. 5 • March 2005
Back to Top