On certain sums over primes and the Riesz function - Patkowski, Alexander (Matematychni Studii, 2026)
We offer some comments on series involving the Mobius 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.