Abstract
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).
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Acknowledgements
We would like to thank Professor A. Krieg for helpful comments on the proof of the modularity of F∣U(p). We also thank Professor M. Amou for pointing out the transcendency of log p (2p−1).
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Communicated by U. Kühn.
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Kikuta, T., Nagaoka, S. On p-adic quaternionic Eisenstein series. Abh. Math. Semin. Univ. Hambg. 83, 147–157 (2013). https://doi.org/10.1007/s12188-013-0084-0
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DOI: https://doi.org/10.1007/s12188-013-0084-0