On some p-adic power series attached to the arithmetic of Q(ζp)

Let p be an odd prime number and let theta be a nontrivial even character of the Galois group of Q(zeta(p))/Q. We prove that the derivative of the Iwasawa power series f (T, theta) is not congruent to zero modulo p, where f (T, theta) is associated to the p-adic L-function L-p(s, theta). (C) 2006 Elsevier Inc. All rights reserved.