On $p$-adic quaternionic Eisenstein series

Details On $p$-adic quaternionic Eisenstein series On $p$-adic quaternionic Eisenstein series

2011-03-14

arxiv.org/abs/1103.2806v1

Mathematics

Number Theory

Scientific paper

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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