Units In Algebraic Fields Research Articles

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

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.

On an algorithm of Billevich for finding units in algebraic fields

The well-known algorithm of Billevich for finding units in algebraic number fields is derived by algebraic methods. Some tables of units in cubic and quartic fields are given.