Riemann's Auxiliary Function. Right limit of zeros
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914831277228032 |
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| author | de Reyna, Juan Arias |
| author_facet | de Reyna, Juan Arias |
| contents | Numerical data suggest that the zeros $ρ$ of the auxiliary Riemann function in the upper half-plane satisfy $\mathop{\mathrm{Re}}(ρ)<1$. We show that this is true for those zeros with $\mathop{\mathrm{Im}}(ρ)> 3.9211\dots10^{65}$. We conjecture that this is true for all of them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Riemann's Auxiliary Function. Right limit of zeros de Reyna, Juan Arias Number Theory Primary 11M06, Secondary 30D99 Numerical data suggest that the zeros $ρ$ of the auxiliary Riemann function in the upper half-plane satisfy $\mathop{\mathrm{Re}}(ρ)<1$. We show that this is true for those zeros with $\mathop{\mathrm{Im}}(ρ)> 3.9211\dots10^{65}$. We conjecture that this is true for all of them. |
| title | Riemann's Auxiliary Function. Right limit of zeros |
| topic | Number Theory Primary 11M06, Secondary 30D99 |
| url | https://arxiv.org/abs/2406.07014 |