We introduce a formula for the p-adic Siegel-Eisenstein series which demonstrates a connection with the genus theta series and the twisted Eisenstein series with level p. We then prove a generalization of Serre's formula in the elliptic modular case. © 2003 Elsevier Inc. All rights reserved.
Katsurada, H., & Nagaoka, S. (2004). On some p-adic properties of Siegel-Eisenstein series. Journal of Number Theory, 104(1), 100–117. https://doi.org/10.1016/S0022-314X(03)00160-4