On some p-adic power series attached to the arithmetic of $\mathbb{Q}(\zeta \mathrm{\_}p)\mathrm{.}$

In this paper, we prove that the derivative of the Iwasawa power series associated to p-adic L-functions of $\mathbb{Q}(\zeta \mathrm{\_}p)$ are not divisible by p. This extends previous results obtained by Ferrero and Washington in 1979.