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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2405.16723 |
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| _version_ | 1866917676258951168 |
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| author | Goto, Akihiro |
| author_facet | Goto, Akihiro |
| contents | Lehmer conjectured that Ramanujan's tau function never vanishes. As a variation of this conjecture, it is proved that \begin{equation*} τ(n)\neq \pm \ell, \pm 2\ell, \pm 2\ell^2, \end{equation*} where $\ell<100$ is an odd prime, by Balakrishnan, Ono, Craig, Tsai and many people. We have proved that \begin{equation*} τ(n)\neq \pm \ell, \pm 2\ell, \pm 4\ell, \pm 8\ell \end{equation*} for any $n\geq 1$ except 14 cases, where $\ell<1000$ is an odd prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16723 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some values which do not belong to the image of Ramanujan's tau-function Goto, Akihiro Number Theory Lehmer conjectured that Ramanujan's tau function never vanishes. As a variation of this conjecture, it is proved that \begin{equation*} τ(n)\neq \pm \ell, \pm 2\ell, \pm 2\ell^2, \end{equation*} where $\ell<100$ is an odd prime, by Balakrishnan, Ono, Craig, Tsai and many people. We have proved that \begin{equation*} τ(n)\neq \pm \ell, \pm 2\ell, \pm 4\ell, \pm 8\ell \end{equation*} for any $n\geq 1$ except 14 cases, where $\ell<1000$ is an odd prime. |
| title | On some values which do not belong to the image of Ramanujan's tau-function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.16723 |