Simon Kristensen, Mathias L. Laursen
We obtain general criteria for giving a lower bound on the degree of numbers of the form [Formula: see text] or of the form [Formula: see text], where the [Formula: see text] and [Formula: see text] are assumed to be algebraic integers, and the [Formula: see text] and [Formula: see text] are natural numbers. In each case, we give a lower bound of the degree over the smallest extension of [Formula: see text] containing all algebraic numbers in the expression. The criteria obtained depend on growth conditions on the involved quantities.