Waring Numbers of Ramified $p$-adic Rings

Lucas Anthony, Joe Burton, Irene Deegbe +5

Let $p$ be prime and $e,k$ be positive integers, and let $R={\mathbb{Z}}_p[\sqrt[e]{p}]$. We calculate the Waring numbers $g_R(k)$ for many values of $p,e$, and $k$, and investig…