The Length of Totally Positive Algebraic-Integers Original Research Article

For totally positive algebraic integers α of degree d(α), we study the set of values of R1(α)1/d(α), where R1(α) denotes the length of the minimal polynomial of α. We find the five smallest elements of this set, as well as a small limit point l. We also show that this set is everywhere dense in (l, ∞).