Norms of indecomposable integers in real quadratic fields

摘要

We study totally positive, additively indecomposable integers in a real quadratic field Q(root D). We estimate the size of the norm of an indecomposable integer by expressing it as a power series in u(i)(-1), where root D has the periodic continued fraction expansion [u(0), (u(1), u(2), ..., u(s-1), 2u(0)) over bar]. This enables us to disprove a conjecture of Jang-Kim [JK] concerning the maximal size of the norm of an indecomposable integer. (C) 2016 Elsevier Inc. All rights reserved.