k-Hypermonogenic automorphic forms

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• 作者：D. Constales ; R.S. Krau&#xdf ; har ; John Ryan
• 关键词：k-Hypermonogenic automorphic forms ; Maa&#xdf ; wave forms ; Eisenstein series ; Fourier expansion ; Laplace– ; Beltrami operator
• 刊名：Journal of Number Theory
• 出版年：2007
• 出版时间：October 2007
• 年：2007
• 卷：126
• 期：2
• 页码：254-271
• 全文大小：196 K

文摘

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.