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

Elon Lindenstrauss*, Amir Mohammadi, Zhiren Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)181-234
Number of pages54
JournalJournal d'Analyse Mathematique
Volume151
Issue number1
DOIs
StatePublished - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023, The Hebrew University of Jerusalem.

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