Hyperbolic Summation for Fractional Sums

2022/12/11 by Meselem Karras, Ling Li, Karras, Meselem +2
Mathematics · #11A25 #11L07 #11N37 #Analytic and geometric function theory #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2212.05443

openalex publication_date 2022/12/11 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28

Abstract

Let f(n) be an arithmetic function with f(n) ≪ n^α for some α∈[0,1) and let \lfloor .\rfloor denote the integer part function. In this paper, we evaluate asymptotically the sums ∑_n₁n₂≤ xf ( \lfloor \fracxn₁n₂ \rfloor ), we use the estimation of three-dimensional exponential sums due to Robert and Sargos.

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