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

Elon Lindenstrauss; Amir Mohammadi; Zhiren Wang

doi:10.1007/s11854-023-0332-x

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

Elon Lindenstrauss^*, Amir Mohammadi, Zhiren Wang

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	181-234
Number of pages	54
Journal	Journal d'Analyse Mathematique
Volume	151
Issue number	1
DOIs	https://doi.org/10.1007/s11854-023-0332-x
State	Published - Dec 2023

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© 2023, The Hebrew University of Jerusalem.

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

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