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arXiv research

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3 results for “Birch-Swinnerton-Dyer”

Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curvesmath.NT

Machine learning predicts Shafarevich-Tate group orders of elliptic curves.

problem Predicting the order of the Shafarevich-Tate group of elliptic curves.

method Train feed-forward neural network and regression models on elliptic curve invariants.

result Models achieve high accuracy (

> 0.9

) and predict orders not seen during training.

Machine Learning Elliptic Curves Shafarevich-Tate Group Birch-Swinnerton-Dyer Conjecture LMFDB

2024-12-24abs ↗pdf ↗

Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyermath.NT

Empirical analysis is often the first step towards the birth of a conjecture. This is the case of the Birch-Swinnerton-Dyer (BSD) Conjecture describing the rational points on an elliptic curve, one of the most celebrated unsolved problems in mathematics. Here we extend the original empirical approach, to the analysis o…

2019-11-04abs ↗pdf ↗

Murmurations: a case study in AI-assisted mathematicsmath.NT

New arithmetic phenomenon 'murmurations' detected using AI.

problem Detecting new arithmetic patterns in large datasets.

method Machine learning interpretability tools (PCA, saliency, convolutional filters).

result Murmurations encode Frobenius traces and connect to number theory.

murmurations arithmetic statistics Frobenius traces Birch-Swinnerton-Dyer random matrix theory

2026-03-10abs ↗pdf ↗