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On certain sums over primes and the Riesz function
Published 19 Aug 2025 in math.NT | (2508.13449v1)
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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