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k-hypermonogenic automorphic forms

Denis Constales·Rolf Soeren Krausshar·John Ryan
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Abstract

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.

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Denis Constales, Rolf Soeren Krausshar, John Ryan. 2006-03-31. k-hypermonogenic automorphic forms. https://arxiv.org/abs/math/0602500

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