Subcoordinate representation of -adic functions and generalization of Hensel's lemma

Abstract

In this paper we describe a new representation of -adic functions, the so-called subcoordinate representation. The main feature of the subcoordinate representation of a -adic function is that the values of the function are given in the canonical form of the representation of -adic numbers. The function itself is determined by a tuple of -valued functions from the set into itself and by the order in which these functions are used to determine the values of . We also give formulae that enable one to pass from the subcoordinate representation of a -Lipschitz function to its van der Put series representation. The effective use of the subcoordinate representation of -adic functions is illustrated by a study of the feasibility of generalizing Hensel's lemma.