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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2508.13449 |
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| _version_ | 1866918413750763520 |
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| author | Patkowski, Alexander E. |
| author_facet | Patkowski, Alexander E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On certain sums over primes and the Riesz function Patkowski, Alexander E. Number Theory 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. |
| title | On certain sums over primes and the Riesz function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.13449 |