A three gap theorem for the adeles

2021/07/11 by Akshat Das, Das, Akshat, Alan Haynes +1
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2107.05147

openalex publication_date 2021/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a natural generalization of the classical three gap theorem, for rotations on adelic tori. Our proof is an adaptation to the adeles of the lattice based approach to gaps problems in Diophantine approximation originally introduced by Marklof and Strömbergsson.

Related

• Bounded remainder sets for rotations on the adelic torus
• The Three Gap Theorem and Riemannian Geometry
• The three gap theorem and the space of lattices
• The frequency problem of the three gap theorem
• The Three Gap Theorem, Interval Exchange Transformations, and Zippered Rectangles