Journal of number theory vol:126 issue:2 pages:254-271
In this paper we deal with monogenic and k-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 k-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 k-hypermonogenic Eisenstein series which provide us with the simplest non-vanishing examples of k-hypermonogenic automorphic forms.