Fields with large Kronecker constants

The Mahler measure of algebraic numbers: a survey

“…The Kronecker constant. Callahan, Newman and Sheingorn [48] define the Kronecker constant of a number field K to be the least ε > 0 such that α ≥ 1 + ε for every algebraic integer α ∈ K. The truth of the SchinzelZassenhaus conjecture (8) [29], with four more found in [30]. Recall that these are positive reciprocal algebraic integers of degree at least 4 having only one conjugate (the number itself) outside the unit circle.…”

“…The Kronecker constant. Callahan, Newman and Sheingorn [48] define the Kronecker constant of a number field K to be the least ε > 0 such that α ≥ 1 + ε for every algebraic integer α ∈ K. The truth of the Schinzel-Zassenhaus conjecture (8) would imply that the Kronecker constant of K is at least c/[K : Q]. They give [48, Theorem 2] a sufficient condition on K for this to be the case.…”

Survey on Lehmer Problems

“…Other cases have confirmed that bound 1.5 or even better bounds can be true. See for example [CNS77], [Mig78], [Rob65].…”