Bounds on certain Higher-Dimensional Exponential Sums via the Self-Reducibility of the Weil Representation

Details Bounds on certain Higher-Dimensional Exponential Sums via the Self-Reducibility of the Weil Representation Bounds on certain Higher-Dimensional Exponential Sums via the Self-Reducibility of the Weil Representation

2006-12-26

arxiv.org/abs/math/0612765v2

Mathematics

Representation Theory

Scientific paper

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.

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