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 of radius R with a constant magnetic field B in the perpendicular direction. We show that, in the limit and , where ν is the Landau level filling factor, we have with . The factor is obtained through the solution of an extreme-value problem in measure theory. Received: 10 November 1998 / Accepted: 27 January 1999