Volume 36 • Number 4 • 2013   • An Ultrametric Lethargy Result and Its Application to $p$-Adic Number Theory J. M. Almira Abstract. In this paper we show a lethargy result in the non-Archimedean 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 $\leq n$ decays slowly. 2010 Mathematics Subject Classification: 46S10, 41A65, A1A25, 11J61, 11J81, 11K60 Full text: PDF