The energy of dilute Bose gases

For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L¹-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(ρ) ≥ 4π a ρ²(1 + 12815√π √ρ a³ + o(√ρ a³)), thereby proving the Lee-Huang-Yang formula for the energy density.