Computational Methods and Function Theory 2 (2002), No. 2, 299--318
Copyright Heldermann Verlag 2002
Rolf Sören Kraußhar
krauss@cage.rug.ac.be, Department of Mathematical Analysis, Ghent University, Building S-22, Galglaan 2, B-9000 Ghent, Belgium.
In this paper we deal with monogenic and $k$-monogenic Clifford-valued automorphic forms in two and several vector variables. We focus on the construction of several families of Eisenstein and Poincar\'{e} series within the setting of this function theory. The functions that we construct provide non-trivial examples for generalizations of the classical Hilbert modular forms within the framework of real and complex Clifford analysis.
Keywords: Monogenic Hilbert modular forms, biregular functions, Clifford analysis, several iterated Dirac operators, higher dimensional automorphic forms.
MSC 2000: Primary: 30G35; Secondary: 11F03, 11F41, 11M36.
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