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arXiv · 2305.18261

Quantitative equidistribution and the local statistics of the spectrum of a flat torus

Elon Lindenstrauss·Amir Mohammadi·Zhiren Wang
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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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Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang. 2023-05-29. Quantitative equidistribution and the local statistics of the spectrum of a flat torus. https://arxiv.org/abs/2305.18261

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