On the square-free representation function of a norm form and   nilsequences
  We show that the restriction to square-free numbers of the representation function attached to a norm form does not correlate with nilsequences. By combining this result with previous work of Browning and the author, we obtain an application that is used in recent work of Harpaz and Wittenberg on the fibration method for rational points. 
Lilian Matthiesen
math.NT