On certain sums of number theory

2020/09/12 by Bordellès, Olivier · 1 citation
#11L07 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2009.05751

Abstract

We study sums of the shape ∑_{n \leqslant x} f ( \lfloor x/n \rfloor ) where f is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We improve previous estimates when f = Λ and f = τ, and provide new results when f = τ_r with r \geqslant 3, breaking the (1)/(2)-barrier in each case. The functions f=μ², f=2^ω and f=ω are also investigated.

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