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

Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)181-234
Number of pages54
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - Dec 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • General Mathematics

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