On some p-adic power series attached to the arithmetic of image Original Research Article

Let p be an odd prime number and let θ be a nontrivial even character of the Galois group of image. We prove that the derivative of the Iwasawa power series f(T,θ) is not congruent to zero modulo p, where f(T,θ) is associated to the p-adic L-function Lp(s,θ).