On certain sums over primes and the Riesz function
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.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Identities
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Matematychni Studii
- Volume
- 65
- Issue
- 1
- Pages
- 3–9
- Publication date
- 25 March 2026
- Language
- UK