Bounds on certain Higher-Dimensional Exponential Sums via the Self-Reducibility of the Weil Representation
Representation Theory
2010-02-08 v2 Mathematical Physics
math.MP
Chaotic Dynamics
Quantum Physics
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.
Keywords
Cite
@article{arxiv.math/0612765,
title = {Bounds on certain Higher-Dimensional Exponential Sums via the Self-Reducibility of the Weil Representation},
author = {Shamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:math/0612765},
year = {2010}
}