Conductors of fractional ideals in Burnside rings for cyclic p-groups and their zeta function

This study is part of the zeta function of the Burnside ring study. The main objective of this paper is to determine the conductors of all isomorphism classes of fractional ideals of finite index in Bp(Cp^n ) the Burnside ring for cyclic groups of order p^n, which leads to a new explicit formula for ζBp(Cp^n )(s) the zeta function of Bp(Cp^n ), and we present a conjecture in which we establish when a fractional ideal M of Bp(Cp^n ) has a Zp-order structure, according to its ZBp(Cp^n ) (M; s) function.