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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.16723 |
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Table of 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.