On natural radii of 𝑝-adic convergence

Abstract

We study the radius of <italic>p</italic>-adic convergence of power series which represent algebraic functions. We apply the <italic>p</italic>-adic theory of ordinary linear differential equations to show that the radius of convergence is the natural one, provided the degree of the function is less than <italic>p</italic>. The study of similar questions for solutions of linear differential equations is indicated.