A question of Erdös on $3$-powerful numbers and an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914742049701888 |
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| author | Walsh, P. G. |
| author_facet | Walsh, P. G. |
| contents | We describe how the Mordell-Weil group of rational points on a certain family of elliptic curves give rise to solutions to a conjecture of Erdös on $3$-powerful numbers, and state a related conjecture which can be viewed as an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A question of Erdös on $3$-powerful numbers and an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture Walsh, P. G. Number Theory 11D25 We describe how the Mordell-Weil group of rational points on a certain family of elliptic curves give rise to solutions to a conjecture of Erdös on $3$-powerful numbers, and state a related conjecture which can be viewed as an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture. |
| title | A question of Erdös on $3$-powerful numbers and an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture |
| topic | Number Theory 11D25 |
| url | https://arxiv.org/abs/2404.03970 |