Minimal polynomial dynamics on the p-adic integers

초록

In this talk, we present a method of characterizing minimal polynomials on the ring ${\mathbb{Z}}_p$ of $p$-adic integers in terms of their coefficients for an arbitrary prime $p$. We first revisit and provide alternative proofs of the known minimality criteria given by Larin \cite{La} for $p=2$ and by Durand and Paccaut \cite{DP} for $p=3$, and then show that for any prime $p\ge 5,$ the proposed method enables us to classify all possible minimal polynomials on $\text{Zp}$ in terms of their coefficients, provided that two prescribed prerequisites for minimality are satisfied.