Calculation of fundamental units of number rings by means of the generalized continued fraction

A. D. Bruno


Abstract: We consider the global generalization of continued fraction which gives the best Diophantine approximations. The way of calculation of the fundamental units of algebraic rings and the way of finding the all solutions for some class of Diophantine equations are based on it. Some examples in dimensions 2, 3, 4 are presented.

Keywords: generalization of continued fraction, Diophantine approximations, set of fundamental units, fundamental domain, Diophantine equation.

UDC: 517.36

DOI: 10.20948/prepr-2017-46