Stoimenow’s log-concavity-without-gaps conjecture for the Alexander polynomial of alternating links

Prove that for any alternating link L with Conway-normalized Alexander polynomial Δ_L(t) = Σ_{k=-n}^{n} a_k t^k, the sequence of absolute values |a_k| is log-concave and has no internal zeros.

Background

Stoimenow strengthened Fox’s unimodality conjecture by proposing that the absolute values of the Alexander polynomial’s coefficients not only be unimodal but satisfy the stronger property of log-concavity and contain no internal zeros. This would imply the trapezoidal shape and unimodality of the sequence.