Bounds on certain Higher-Dimensional Exponential Sums via the   Self-Reducibility of the Weil Representation
  We describe a new method to bound certain higher-dimensional exponential sums which are associated with tori in symplectic groups over finite fields. Our method is based on the self-reducibility property of the Weil representation. As a result, we obtain a sharp form of the Hecke quantum unique ergodicity theorem for generic linear symplectomorphisms of the 2N-dimensional torus. 
Shamgar Gurevich (IAS) and Ronny Hadani (Austin)