Publication at Faculty of Mathematics and Physics |
2020
Abstract
LetK=Q(D)\documentclass be a real quadratic field. We consider the additive semigroupOK+(+)\documentclass of totally positive integers inKand determine its generators (indecomposable integers) and relations; they can be nicely described in terms of the periodic continued fraction forD\documentclass.
We also characterize all uniquely decomposable integers inKand estimate their norms. Using these results, we prove that the semigroupOK+(+)\documentclass completely determines the real quadratic fieldK.