Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos
Abstract
In these notes we discuss the "self-reducibility property" of the Weil representation. We explain how to use this property to obtain sharp estimates of certain higher-dimensional exponential sums which originate from the theory of quantum chaos. As a result, we obtain the Hecke quantum unique ergodicity theorem for generic linear symplectomorphism A of the torus $T2N=R2N/Z2N.
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