A Selberg trace formula for hypercomplex analytic cusp forms

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 for...

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Veröffentlicht in:Journal of number theory Jg. 148; S. 398 - 428
Hauptverfasser: Grob, D., Kraußhar, R.S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.03.2015
Schlagworte:
Clifford algebras
Dimension formulas for modular forms
Dirac type operators
Hyperbolic harmonic functions
Hypercomplex cusp forms
Selberg trace formula
11F03
Dimension formulas for modular forms
11F72
Hypercomplex cusp forms
Dirac type operators
30G35
35J05
Clifford algebras
Selberg trace formula
11F55
Hyperbolic harmonic functions
ISSN:0022-314X, 1096-1658
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Zusammenfassung: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.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2014.09.002