Infinite Product of the Riemann auxiliary function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913394469109760 |
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| author | de Reyna, Juan Arias |
| author_facet | de Reyna, Juan Arias |
| contents | We obtain the product for the auxiliary function $\mathop{\mathcal R}(s)$ and study some related functions as its phase $ω(t)$ at the critical line. The function $ω(t)$ determines the zeros of $ζ(s)$ on the critical line. We study the influence of the zeros of $\mathop{\mathcal R}(s)$ on $ω(t)$. Thus, the relationship between the zeros of $\mathop{\mathcal R}(s)$ and those of $ζ(s)$ is determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite Product of the Riemann auxiliary function de Reyna, Juan Arias Number Theory Primary 11M06, Secondary 30D99 We obtain the product for the auxiliary function $\mathop{\mathcal R}(s)$ and study some related functions as its phase $ω(t)$ at the critical line. The function $ω(t)$ determines the zeros of $ζ(s)$ on the critical line. We study the influence of the zeros of $\mathop{\mathcal R}(s)$ on $ω(t)$. Thus, the relationship between the zeros of $\mathop{\mathcal R}(s)$ and those of $ζ(s)$ is determined. |
| title | Infinite Product of the Riemann auxiliary function |
| topic | Number Theory Primary 11M06, Secondary 30D99 |
| url | https://arxiv.org/abs/2406.12344 |