On the Image of the $p$-adic Logarithm on Annuli of Principal Units

Mabud Ali Sarkar

Let $K$ be a finite extension of ${\mathbb{Q}}_p$, and let ${\mathfrak{m}}_K$ be its maximal ideal. The image of the group of principal units $1+{\mathfrak{m}}_K$ under $p$-adic logarith…