Summary
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 a generic linear symplectomorphism A of the torus \({\mathbb{T} = \mathbb{R}}^{2N}/{\mathbb{Z}}^{2N}.\)
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Gurevich, S., Hadani, R. (2010). Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos. In: Ceyhan, Ö., Manin, Y.I., Marcolli, M. (eds) Arithmetic and Geometry Around Quantization. Progress in Mathematics, vol 279. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4831-2_7
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