Learning Euler Factors of Elliptic Curves
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916614393298944 |
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| author | Babei, Angelica Charton, François Costa, Edgar Huang, Xiaoyu Lee, Kyu-Hwan Lowry-Duda, David Narayanan, Ashvni Pozdnyakov, Alexey |
| author_facet | Babei, Angelica Charton, François Costa, Edgar Huang, Xiaoyu Lee, Kyu-Hwan Lowry-Duda, David Narayanan, Ashvni Pozdnyakov, Alexey |
| contents | We apply transformer models and feedforward neural networks to predict Frobenius traces $a_p$ from elliptic curves given other traces $a_q$. We train further models to predict $a_p \bmod 2$ from $a_q \bmod 2$, and cross-analysis such as $a_p \bmod 2$ from $a_q$. Our experiments reveal that these models achieve high accuracy, even in the absence of explicit number-theoretic tools like functional equations of $L$-functions. We also present partial interpretability findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Euler Factors of Elliptic Curves Babei, Angelica Charton, François Costa, Edgar Huang, Xiaoyu Lee, Kyu-Hwan Lowry-Duda, David Narayanan, Ashvni Pozdnyakov, Alexey Number Theory Machine Learning We apply transformer models and feedforward neural networks to predict Frobenius traces $a_p$ from elliptic curves given other traces $a_q$. We train further models to predict $a_p \bmod 2$ from $a_q \bmod 2$, and cross-analysis such as $a_p \bmod 2$ from $a_q$. Our experiments reveal that these models achieve high accuracy, even in the absence of explicit number-theoretic tools like functional equations of $L$-functions. We also present partial interpretability findings. |
| title | Learning Euler Factors of Elliptic Curves |
| topic | Number Theory Machine Learning |
| url | https://arxiv.org/abs/2502.10357 |