On the ground state energy of the delta-function Fermi gas
  The weak coupling asymptotics to order $\gamma$ of the ground state energy of the delta-function Fermi gas, derived heuristically in the literature, is here made rigorous. Further asymptotics are in principle computable. The analysis applies to the Gaudin integral equation a method previously used by one of the authors for the asymptotics of large Toeplitz matrices. 
Craig A. Tracy, Harold Widom
math-ph math.MP