Exceptional sets for Diophantine inequalities
  We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N^{1-c}), for a positive number c. 
Scott T. Parsell and Trevor D. Wooley
math.NT