A Selberg trace formula for hypercomplex analytic cusp forms

JOURNAL OF NUMBER THEORY

卷:148

Article

Grob, D.¹  Krausshar, R. S.² 

[1] Rhein Westfal TH Aachen, Lehrstuhl Math, D-52056 Aachen, Germany

[2] Univ Erfurt, Erziehungswissensch Fak, D-99089 Erfurt, Germany

关键词: Selberg trace formula;    Dimension formulas for modular forms;    Hypercomplex cusp forms;    Hyperbolic harmonic functions;    Dirac type operators;    Clifford algebras;   

DOI  :  10.1016/j.jnt.2014.09.002

来源: Elsevier

【 摘 要 】

A breakthrough in developing a theory of hypercomplex analytic modular forms over Clifford algebras has been the proof of the existence of non-trivial cusp forms for important discrete arithmetic subgroups of the Ahlfors-Vahlen group. Hypercomplex analytic modular forms in turn also include Maass forms associated to particular eigenvalues as special cases. In this paper we establish a Selberg trace formula for this new class of automorphic forms. In particular, we show that the dimension of the space of hypercomplex-analytic cusp forms is finite. Finally, we describe the space of Eisenstein series and give a dimension formula for the complete space of k-holomorphic Cliffordian modular forms. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free