2023/04/05 by Reynold Fregoli, Fregoli, Reynold
Computer Science · Mathematics · #11H16 #11J13 #11P21 #Analytic Number Theory Research #Bayesian Methods and Mixture Models #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2304.02566
openalex publication_date 2023/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an estimate for the number of lattice points lying in certain non-convex Euclidean domains of interest in Diophantine approximation. As an application, we generalise a result of Kruse (1964) concerning the almost sure order of magnitude of sums of reciprocals of fractional parts and solve a conjecture posed by Beresnevich, Haynes, and Velani. The methods are based both on the geometry of numbers and on probability theory.