Trace funcions and Galois invariant $p$-adic measures

Abstract

Let p be a prime number, Qp the field of p-adic numbers, Qp a fixed algebraic closure of Qp, and Cp the completion of Qp with respect to the p-adic valuation. We study trace functions associated to p-adic measures defined on compact subsets of Cp which are invariant under the action of the Galois group G = Galcont(Cp/Qp).