Quantitative equidistribution and the local statistics of the spectrum of a flat torus
Journal d'Analyse Mathématique(2023)
Abstract
We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate. The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.
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Key words
flat torus,quantitative equidistribution,local statistics,spectrum
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