Zeta Functions of Burnside Rings of Groups of Order p and p2

The purpose of this article is to determine B(G)(s) the zeta function of B(G) the Burnside ring, for the cyclic groups G=Cp and Cp2, where p is a prime integer, in order to see its behavior and make conjectures for further research. We study thoroughly all ideals of finite index in the (p)-order B(p)(G), to find B(p)(G)(s). Furthermore, we compute the polynomial f(G)(p-s), that belongs to [p-s] and relates B(p)(G)(s) to [image omitted] the zeta function of the maximal order [image omitted].