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Mathematics > Representation Theory

arXiv:math/0612765 (math)
[Submitted on 26 Dec 2006 (v1), last revised 8 Feb 2010 (this version, v2)]

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

Authors:Shamgar Gurevich (IAS), Ronny Hadani (Austin)
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Abstract: 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.
Subjects: Representation Theory (math.RT); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD); Quantum Physics (quant-ph)
Cite as: arXiv:math/0612765 [math.RT]
  (or arXiv:math/0612765v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.math/0612765

Submission history

From: Shamgar Gurevich [view email]
[v1] Tue, 26 Dec 2006 11:09:42 UTC (43 KB)
[v2] Mon, 8 Feb 2010 00:24:26 UTC (31 KB)
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