Simple bounds for the auxiliary function of Riemann
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914863134015488 |
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| author | de Reyna, Juan Arias |
| author_facet | de Reyna, Juan Arias |
| contents | We give simple numerical bounds for $ζ(s)$, $\vartheta(s)$, $\mathop{\mathcal R}(s)$, $Z(t)$, for use in the numerical computation of these functions.
The purpose of the paper is to give bounds for several functions needed in the calculation of $ζ(s)$ and $Z(t)$. We are not pretending to have any originality. Our object is to be useful as a reference in our work for simple (simple to compute and simple to check) bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple bounds for the auxiliary function of Riemann de Reyna, Juan Arias Number Theory Primary 11M06, Secondary 30D99 We give simple numerical bounds for $ζ(s)$, $\vartheta(s)$, $\mathop{\mathcal R}(s)$, $Z(t)$, for use in the numerical computation of these functions. The purpose of the paper is to give bounds for several functions needed in the calculation of $ζ(s)$ and $Z(t)$. We are not pretending to have any originality. Our object is to be useful as a reference in our work for simple (simple to compute and simple to check) bounds. |
| title | Simple bounds for the auxiliary function of Riemann |
| topic | Number Theory Primary 11M06, Secondary 30D99 |
| url | https://arxiv.org/abs/2407.06681 |