Elementary analytic methods in higher ramification theory

This paper offers proofs of a number of standard results in the higher ramification theory of discretely valued fields, using as tools only the Weierstrass Preparation Theorem and the theory of the Newton polygon and copolygon. The propositions proved are the functoriality of the Hasse–Herbrand transition function, Herbrandʼs Theorem, Senʼs Theorem on the rapidity of approach to the identity of successive p-power iterates of an invertible series in characteristic p, and the Hasse–Arf Theorem.