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Murmurations of elliptic curves

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arxiv 2204.10140 v2 pith:D6KBDIIS submitted 2022-04-21 math.NT hep-thstat.ML

Yang-Hui He , Kyu-Hwan Lee , Thomas Oliver , Alexey Pozdnyakov This is my paper · ORCID
classification math.NThep-thstat.ML
keywords curvesellipticaveragerankaccordingclassifyingconductordata-scientific
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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.

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  1. Machine learning automorphic forms for black holes

    hep-th 2025-05 conditional novelty 5.0 of 10

    Feed-forward neural networks trained on Fourier coefficients can predict modular weights for negative-weight powers of eta and E2, and for simple Jacobi theta products, within the training range.

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