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A generalization of the Hasse-Arf theorem.

Let L\K be a totally ramified finite galois extension of a complete field K with respect to a discrete valuation such that the residue class field L of L is a separable extension of the residue class field K of K. Then a class function aG on the galois group G of L/K is defined which turns out to be a character of G called the Artin character attached to L/K. The purpose of this paper is to give an explicit formula of the multiplicity γ(χ) of an absolutely irreducible character χ of G in a^). Namely we prove the following.