Sequences modulo one: convergence of local statistics

2014/10/16 by Ilya Vinogradov, Vinogradov, Ilya
Mathematics · #11J71 #11K36 #37A17 #37D40 #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.DS #math.NT #msc:11J71 #msc:11K36 #msc:37A17 #msc:37D40

paper · pdf · doi:10.48550/arxiv.1410.4346

6 figures. arXiv admin note: text overlap with arXiv:1306.0028

arxiv created 2014/10/16 · openalex publication_date 2014/10/16 · arxiv updated 2014/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey recent results beyond equidistribution of sequences modulo one. We focus on the sequence of angles in a Euclidean lattice in \mathbb R² and on the sequence √ n\bmod1 .

Citations

• The distribution of directions in an affine lattice: two-point correlations and mixed moments

Related

• On uniform distribution modulo one
• Distribution modulo one and Ratner's theorem
• Local limit theorems and mod-phi convergence
• Square roots and lattices
• Mod-ϕ convergence