On p-adic quaternionic Eisenstein series

On p-adic quaternionic Eisenstein series

We show that certain p -adic Eisenstein series for quaternionic modular groups of degree 2 become “real” modular forms of level p in almost all cases. To prove this, we introduce a U ( p ) type operator. We also show that there exists a p -adic Eisenstein series of the above type that has transcende...

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Veröffentlicht in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2013-10, Vol.83 (2), p.147-157
Hauptverfasser: Kikuta, Toshiyuki, Nagaoka, Shoyu
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Differential Geometry
Geometry
Mathematics
Mathematics and Statistics
Number Theory
Topology
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Zusammenfassung:We show that certain p -adic Eisenstein series for quaternionic modular groups of degree 2 become “real” modular forms of level p in almost all cases. To prove this, we introduce a U ( p ) type operator. We also show that there exists a p -adic Eisenstein series of the above type that has transcendental coefficients. Former examples of p -adic Eisenstein series for Siegel and Hermitian modular groups are both rational (i.e., algebraic).
ISSN:0025-5858
1865-8784
DOI:10.1007/s12188-013-0084-0