On the ground state energy of the fractional quantum Hall effect

Let I (N, R) be the ground state energy of N electrons confined to a disc o f radius R with a constant magnetic field B in the perpendicular direction. We show that, in the limit R --> infinity and N/R-2 --> nu, where nu is th e Landau level filling factor, we have I (N, R) = (pi/4)lambda root nu N-3/ 2 + o(N-3/2) with lambda = (2e(3)m(e)(2)c/(h) over bar(3)\B\)(1/2). The fac tor pi/4 = (1/2).(pi/2) is obtained through the solution of an extreme-valu e problem in measure theory.