Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves

arXiv:2603.17681 · math.NT, stat.ML · Submitted 2026-03-18 · Read on arXiv

math.NT, stat.ML

Submitted: 2026-03-18

Updated: 2026-09-25

Code: https://github.com/yidiq7/murmurationscnn

Terminology

• Accuracy — 19× in this paper · explained in 1 episode
• Trace — 6× in this paper · explained in 2 episodes
• 1D CNN — 3× in this paper · explained in 2 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• Machines Learn Number Fields, But How? The Case of Galois Groups
• Learning Fricke signs from Maass form Coefficients
• Machine learning the vanishing order of rational L-functions
• Murmurations of Maass forms
• New Rank Records For Elliptic Curves Having Rational Torsion
• Predicting root numbers with neural networks
• Murmurations

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