Publikace na Matematicko-fyzikální fakulta |
2016
Abstrakt
We study totally positive, additively indecomposable integers in a real quadratic field Q(D MINUS SIGN MINUS SIGN SQUARE ROOT ). We estimate the size of the norm of an indecomposable integer by expressing it as a power series in u MINUS SIGN 1 i , where D MINUS SIGN MINUS SIGN SQUARE ROOT has the periodic continued fraction expansion [u 0 ,u 1 ,u 2 ,...,u sMINUS SIGN 1 ,2u 0 ,u 1 ,u 2 ,...].
This enables us to disprove a conjecture of Jang-Kim [JK] concerning the maximal size of the norm of an indecomposable integer.