Bounding the integral of the argument of the Riemann Zeta function
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918270722899968 |
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| author | Amberger, Victor |
| author_facet | Amberger, Victor |
| contents | This article improves the estimate of $|S_1(t_2)-S_1(t_1)|$, which is the definite integral of the argument of the Riemann zeta-function between $t_1$ and $t_2$. Estimates of this quantity are needed to apply Turing's method to compute the exact number of zeta zeros up to a given height. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounding the integral of the argument of the Riemann Zeta function Amberger, Victor Number Theory 11M26 This article improves the estimate of $|S_1(t_2)-S_1(t_1)|$, which is the definite integral of the argument of the Riemann zeta-function between $t_1$ and $t_2$. Estimates of this quantity are needed to apply Turing's method to compute the exact number of zeta zeros up to a given height. |
| title | Bounding the integral of the argument of the Riemann Zeta function |
| topic | Number Theory 11M26 |
| url | https://arxiv.org/abs/2512.23064 |