Quadratic approximation in ℚp
Yann Bugeaud, Tomislav Pejković · International Journal of Number Theory · 2014
Let p be a prime number. Let w2and [Formula: see text] denote the exponents of approximation defined by Mahler and Koksma, respectively, in their classifications of p-adic numbers. It is well-known that every p-adic number ξ satisfies [Formula: see text], with [Formula: see text] for almost all ξ. By means of Schneider's continued fractions, we give explicit examples of p-adic numbers ξ for which the function [Formula: see text] takes any prescribed value in the interval (0, 1].