On general sums involving the floor function with applications to k-free numbers

2021/12/12 by Zhang, Wei
#11L07 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.06156

Abstract

In this paper, we consider sums related the floor function. We can improve some previous results for some special arithmetic functions considered by Bordellés [3], Stucky[9] and Liu-Wu-Yang [6]. We can also give a refined result for previous results for general function considered by Bordellés, Dai, Heyman, Pan and Shparlinski [1] and Wu [11].

Related

• On a family of sums of powers of the floor function and their links with generalized Dedekind sums
• Series and sums involving the floor function
• Some Refinements of Formulae Involving Floor and Ceiling Functions
• An alternating sum of the floor function of square roots
• Certain floor function sums over powers