Murmurations of elliptic curves
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916344883052544 |
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| author | He, Yang-Hui Lee, Kyu-Hwan Oliver, Thomas Pozdnyakov, Alexey |
| author_facet | He, Yang-Hui Lee, Kyu-Hwan Oliver, Thomas Pozdnyakov, Alexey |
| contents | We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking oscillating pattern, the details of which vary with the rank. Based on this observation, we perform various data-scientific experiments with the goal of classifying elliptic curves according to their ranks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10140 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Murmurations of elliptic curves He, Yang-Hui Lee, Kyu-Hwan Oliver, Thomas Pozdnyakov, Alexey Number Theory High Energy Physics - Theory Machine Learning We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking oscillating pattern, the details of which vary with the rank. Based on this observation, we perform various data-scientific experiments with the goal of classifying elliptic curves according to their ranks. |
| title | Murmurations of elliptic curves |
| topic | Number Theory High Energy Physics - Theory Machine Learning |
| url | https://arxiv.org/abs/2204.10140 |