An Ultrametric lethargy result and its application to p-adic number   theory
  In this paper we show a lethargy result in the non-Arquimedian context, for general ultrametric approximation schemes and, as a consequence, we prove the existence of p-adic transcendental numbers whose best approximation errors by algebraic p-adic numbers of degree less than or equal to n decays slowly. 
J. M. Almira
math.NT