  I propose a method for studying the product of bandwidths for the
Harper-Hofstader model. This method requires knowledge of the moments of the
midband energies. I conjectured a general formula for these moments. I computed
the asymptotic representation for the product of bandwidths in the limit of a
weak magnetic flux using Szego's theorem for Hankel matrices. I then give a
first approximation for the edge of the butterfly spectrum and discuss its
connection with P. Levy's formula for Brownian motion .
