2023/05/29 by Elon Lindenstrauss, Amir Mohammadi, Lindenstrauss, Elon +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2305.18261
openalex publication_date 2023/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.