2021/01/26 by Reynold Fregoli, Fregoli, Reynold
Computer Science · Mathematics · #11H16 #11J13 #11Jxx #11P21 #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2101.11094
openalex publication_date 2021/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove new upper bounds for sums of reciprocals of fractional parts over general aligned boxes, thus extending a previous result of the author concerning bounds for sums of reciprocals over symmetric boxes. These new upper bounds depend solely on the volume of the boxes, and not on their diameter. This generalisation relies a novel lattice-point counting technique involving estimates for the higher successive minima of certain naturally arising lattices.