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Quantitative equidistribution and the local statistics of the spectrum of a flat torus
Published 29 May 2023 in math.NT and math.DS | (2305.18261v1)
Abstract: We show that 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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