The energy of dilute Bose gases

For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L-1-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1 + 128/15 root pi root rho a(3) + o(root rho a(3))), thereby proving the Lee-Huang-Yang formula for the energy density.