k-hypermonogenic automorphic forms
arXiv:math/0602500
Abstract
In this paper we deal with monogenic and -hypermonogenic automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. Monogenic automorphic forms are exactly the 0-hypermonogenic automorphic forms. In the first part we establish an explicit relation between -hypermonogenic automorphic forms and Maaß wave forms. In particular, we show how one can construct from any arbitrary non-vanishing monogenic automorphic form a Clifford algebra valued Maaß wave form. In the second part of the paper we compute the Fourier expansion of the -hypermonogenic Eisenstein series which provide us with the simplest non-vanishing examples of -hypermonogenic automorphic forms.
20 pages