On Littlewood"s constants

In two papers, Littlewood studied seemingly unrelated constants: (i) the best alpha such that for any polynomial f, of degree n, the areal integral of its spherical derivative is at most const -n(alpha), and (ii) the extremal growth rate beta of the length of Green's equipotentials for simply connected domains. These two constants are shown to coincide, thus greatly improving known estimates on a.