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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.21021 |
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| _version_ | 1866915176908849152 |
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| author | Kim, Seungki Nguyen, Phong Q. |
| author_facet | Kim, Seungki Nguyen, Phong Q. |
| contents | We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to $\approx \exp(1.96 \times 10^{19})$, which is significantly below the conjectured value of $\approx \exp(5.15 \times 10^{23})$ by Kotnik and van de Lune [KvdL04]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On counterexamples to the Mertens conjecture Kim, Seungki Nguyen, Phong Q. Number Theory We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to $\approx \exp(1.96 \times 10^{19})$, which is significantly below the conjectured value of $\approx \exp(5.15 \times 10^{23})$ by Kotnik and van de Lune [KvdL04]. |
| title | On counterexamples to the Mertens conjecture |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.21021 |