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.
Publié le : 2005-03-14
Classification:
automorphic forms,
arithmetic subgroups of the orthogonal group,
functions of hypercomplex variables,
Dirac operators,
Clifford algebras,
11 F 03,
30 G 35,
11 F 55
@article{1110205631,
author = {Krau\ss har, Rolf S\"oren},
title = {Generalized Analytic Automorphic Forms for some Arithmetic Congruence
subgroups of the Vahlen group on the $n$-Dimensional Hyperbolic Space},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {5},
year = {2005},
pages = { 759-774},
language = {en},
url = {http://dml.mathdoc.fr/item/1110205631}
}
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, Tome 11 (2005) no. 5, pp. 759-774. http://gdmltest.u-ga.fr/item/1110205631/