On certain sums over primes and the Riesz function

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 25 Mar 2026Embargo end date: 01 Aug 2025Publisher:Ivan Franko National University of LvivJournal:Matematychni Studii, volume 65, pages 3-9 (issn: 1027-4634, eissn: 2411-0620,

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Authors: Patkowski, Alexander E.;

doi: 10.30970/ms.65.1.3-9 , 10.48550/arxiv.2508.13449

arXiv: 2508.13449

On certain sums over primes and the Riesz function

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Abstract

We offer some comments on series involving the M$\ddot{o}$bius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by applying Riemann-Stieltjes integration. We offer a new formula connecting the derivative of the Gram series to the Riesz function, which we then use to obtain general integral relationships.

Keywords

Number Theory, FOS: Mathematics, Number Theory (math.NT)

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