Computation of the best Diophantine approximations and of fundamental units of algebraic fields

Abstract

A global generalization of continued fraction that yields the best Diophantine approximations of any dimension is considered. In the algebraic case, this generalization underlies a method for calculating the fundamental units of algebraic rings and the periods of best approximations, as well as the identification of the fundamental domain with respect to these periods. The units of an algebraic field are understood as the units of maximal order of this field.