On the error term in the explicit formulaof Riemann-von Mangoldt II
We give an explicit $O(x/T)$ error term for the truncated Riemann-von Mangoldt explicit formula. For large $x$, this provides a modest improvement over previous work, which we demonstrate via an application to a result on primes between consecutive powers.
Authors
- Daniel R. Johnston (ORCID: https://orcid.org/0000-0001-6507-034X)
- Michaela Cully-Hugill (ORCID: https://orcid.org/0000-0002-4144-1393)
Publication Details
- Journal
- Functiones et Approximatio Commentarii Mathematici
- Published
- 2025-03-14
- DOI
- https://doi.org/10.7169/facm/241110-18-11
- Citations
- 3
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 16.13