On p-adic modularity in the p-adic Heisenberg algebra

We establish existence theorems for the image of the normalized character map of the p-adic Heisenberg algebra S taking values in the algebra of Serre p-adic modular forms M p . In particular, we describe the construction of an analytic family of states in S whose character values are the well-known Λ-adic family of p-adic Eisenstein series of level one built from classical Eisenstein series. This extends previous work treating a specialization …