Work

Murmurations, Mestre–Nagao sums, and convolutional neural networks for elliptic curves

Year: 2026

Type: article

Abstract: We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over $$\mathbb {Q}$$ Q and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki–Vlah, Bujanović–Kazalicki–Novak, and Pozdnyakov, we observe high accuracy predictions for the analytic rank across a range of conductors. We interpret the prediction using saliency curves and explore the interesting interplay between saliency, murmurations and Mestre–Nagao sums.

Source: Research in Number Theory

DOI: 10.1007/s40993-026-00784-5

Authors: Joanna Bieri, Edgar Costa, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, Tamara Veenstra

Institutions: University of Redlands, Massachusetts Institute of Technology, Korea Institute for Advanced Study, University of Connecticut, Brown University, University of Westminster, Northeastern University, Harvard University, The NSF AI Institute for Artificial Intelligence and Fundamental Interactions

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funders: National Science Foundation, Simons Foundation, Harvard University, Science Foundation Ireland, Directorate for Mathematical and Physical Sciences, Division of Mathematical Sciences

Awards: G2366492356, AI Institute: AI Research Institute for Fundamental Interactions, G9000845143, G9000846491

OpenAlex ID: W7139042001

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