Truncated expansion of ${\zeta }_{p^n}$ in the $p$-adic Mal'cev-Neumann field

Shanwen Wang, Yijun Yuan

Fix an odd prime $p$. In this article, we provide a $\mathrm{mod}p$ harmonic number identity, which appears naturally in the canonical expansion of a root ${\zeta }_{p^n}$ of the $p^n$-…