ABSTRACT
In the first half of the 20th century K. Mahler and J. Koksma introduced classification systems for the complex numbers based on their approximation properties. For a given complex number ζ, Mahler’s classification of ζ is determined by how small |P(ζ)| may be when P is a non-zero integral polynomial of degree at most d and height at most h. The Koksma classification of ζ is determined by how small |α − ζ| may be made when α is an algebraic number whose minimal polynomial has degree at most d and height at most h. These two quantities are clearly related since |P(ζ)| is small exactly when ζ is near a root of P(x).
