Discrete Fourier restriction associated with Schrodinger equations
  In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result on Strichartz estimates associated with Schr\"odinger equations on torus. Some sharp estimates on $L^{\frac{2(d+2)}{d}}$ norm of certain exponential sums in higher dimensional cases are established. As an application, we show that some discrete multilinear maximal functions are bounded on $L^2(\mathbb Z)$. 
Yi Hu and Xiaochun Li
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