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arXiv · 2502.10360

Machine learning the vanishing order of rational L-functions

Joanna Bieri·Giorgi Butbaia·Edgar Costa·Alyson Deines·Kyu-Hwan Lee·David Lowry-Duda·Thomas Oliver·Yidi Qi·Tamara Veenstra
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Abstract

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.

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Joanna Bieri, Giorgi Butbaia, Edgar Costa, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, Tamara Veenstra. 2025-02-14. Machine learning the vanishing order of rational L-functions. https://arxiv.org/abs/2502.10360

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