Machine learning the vanishing order of rational L-functions
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arXiv
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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915156873707520 |
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| author | Bieri, Joanna Butbaia, Giorgi Costa, Edgar Deines, Alyson Lee, Kyu-Hwan Lowry-Duda, David Oliver, Thomas Qi, Yidi Veenstra, Tamara |
| author_facet | Bieri, Joanna Butbaia, Giorgi Costa, Edgar Deines, Alyson Lee, Kyu-Hwan Lowry-Duda, David Oliver, Thomas Qi, Yidi Veenstra, Tamara |
| contents | In this paper, we study the vanishing order of rational $L$-functions from a data scientific perspective. Each $L$-function is represented in our data by finitely many Dirichlet coefficients, the normalisation of which depends on the context. We observe murmuration-like patterns in averages across our dataset, find that PCA clusters rational $L$-functions by their vanishing order, and record that LDA and neural networks may accurately predict this quantity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Machine learning the vanishing order of rational L-functions Bieri, Joanna Butbaia, Giorgi Costa, Edgar Deines, Alyson Lee, Kyu-Hwan Lowry-Duda, David Oliver, Thomas Qi, Yidi Veenstra, Tamara Number Theory High Energy Physics - Theory In this paper, we study the vanishing order of rational $L$-functions from a data scientific perspective. Each $L$-function is represented in our data by finitely many Dirichlet coefficients, the normalisation of which depends on the context. We observe murmuration-like patterns in averages across our dataset, find that PCA clusters rational $L$-functions by their vanishing order, and record that LDA and neural networks may accurately predict this quantity. |
| title | Machine learning the vanishing order of rational L-functions |
| topic | Number Theory High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.10360 |