On the $p$-adic transcendence of ${\sum }_{k=1}^{\infty }{p}^{-1/p^k}$

Shanwen Wang, Yijun Yuan

Let $p$ be a prime number. In this article, we prove that the $p$-adic Hahn series ${\sum }_{k=1}^{\infty }{p}^{-1/p^k}$, which is the mixed-characteristic analogue of Abhyankar's solutio…