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arXiv · 2508.13449

On certain sums over primes and the Riesz function

Alexander E. Patkowski
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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.

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Alexander E. Patkowski. 2025-08-19. On certain sums over primes and the Riesz function. https://doi.org/10.30970/ms.65.1.3-9

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