Improved estimates for the discrete Fourier restriction to the higher   dimensional sphere
  We improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\frac{2(n+1)}{n-3}$ to $p=\frac{2n}{n-3}$, when $n\ge 4$. 
Jean Bourgain and Ciprian Demeter
math.CA