An exact way to verify whether n is a congruent number using Heegner points
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909398326050816 |
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| author | Chen, Heng Ma, Rong Du, Tuoping |
| author_facet | Chen, Heng Ma, Rong Du, Tuoping |
| contents | We introduce the relationship between congruent numbers and elliptic curves, and compute the conductor of the elliptic curve $y^2 = x^3 - n^2 x$ associated with it. Furthermore, we prove that its $L$-series coefficient $a_m = 0$ when $m \equiv 3 \mod 4$.By using the invariants of the elliptic curve introduced above, we calculate Heegner points to quickly verify whether $n$ is a congruent number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An exact way to verify whether n is a congruent number using Heegner points Chen, Heng Ma, Rong Du, Tuoping Number Theory 11G18 G.2.0 We introduce the relationship between congruent numbers and elliptic curves, and compute the conductor of the elliptic curve $y^2 = x^3 - n^2 x$ associated with it. Furthermore, we prove that its $L$-series coefficient $a_m = 0$ when $m \equiv 3 \mod 4$.By using the invariants of the elliptic curve introduced above, we calculate Heegner points to quickly verify whether $n$ is a congruent number. |
| title | An exact way to verify whether n is a congruent number using Heegner points |
| topic | Number Theory 11G18 G.2.0 |
| url | https://arxiv.org/abs/2411.14188 |