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 R → ∞ and N/R² → v, where v is the Landau level filling factor, we have I (N, R) = (π/4)λ√vN^3/2 + o(N^3/2) with λ = (2e³m²_ec/(Latin small letter h with stroke)³|B|)^1/2. The factor π/4 = (1/2) · (π/2) is obtained through the solution of an extreme-value problem in measure theory.