  Eisenstein polynomials, which were defined by Oura, are analogues of the
concept of an Eisenstein series. Oura conjectured that there exist some
analogous properties between Eisenstein series and Eisenstein polynomials. In
this paper, we provide new analogous properties of Eisenstein polynomials and
zeta polynomials. These properties are finite analogies of certain properties
of Eisenstein series.
