A formal power series of a Hecke ring associated with the Heisenberg lie algebra over ℤ<inf>p</inf>

This paper studies a formal power series with coefficients in a Hecke ring associated with the Heisenberg Lie algebra. We relate the series to the classical Hecke series defined by Hecke, and prove that the series has a property similar to the rationality theorem of the classical Hecke series. And then, our results recover the rationality theorem of the classical Hecke series.