We study the structure of the $RO(G)$-graded homotopy Mackey functors of any Eilenberg-MacLane spectrum $H\underline{ M}$ for $G$ a cyclic $p$-group. When $\underline{ R}$ is a Green functor, we define orientation classes $u_V$ for $H\underline{ R}$ and deduce a generalized gold relation. We deduce the $a_V,u_V$-isomorphism regions of the $RO(G)$-graded homotopy Mackey functors and prove two induction theorems. As applications, we compute the positive cone of $H\underline{ \mathbb{ A}}$, as well as the positive and negative cones of $H\underline{ \mathbb{ Z}}$. The latter two cones are essential to the slice spectral sequences of $MU^{ ((C_{ 2^n}))}$ and its variants.
Categories: math.AT