Abstract
A method for studying the product of bandwidths for the Harper-Hofstader model is proposed, which requires knowledge of the moments of the midband energies. A general formula for these moments is conjectured, and the asymptotic representation for the product of bandwidths computed in the limit of a weak magnetic flux using Szegö's theorem for Hankel matrices. Then a first approximation for the edge of the butterfly spectrum is given and its connection with Lévy's formula for Brownian motion discussed.