Date of Completion
Spring 5-1-2024
Project Advisor(s)
Kyu-Hwan Lee; Jeremy Teitelbaum; Derek Aguiar
University Scholar Major
Mathematics
Second University Scholar Major
Computer Science
Disciplines
Computer Sciences | Data Science | Mathematics | Number Theory | Theory and Algorithms
Abstract
We report on a machine learning investigation of large datasets of elliptic curves and L-functions. This leads to the discovery of murmurations, an unexpected correlation between the root numbers and Dirichlet coefficients of L-functions. We provide a formal definition of murmurations, describe the connection with 1-level density, and provide three examples for which the murmuration phenomenon has been rigorously proven. Using our understanding of murmurations, we then build new machine learning models in search of a polynomial time algorithm for predicting root numbers. Based on our models and several heuristic arguments, we conclude that it is unlikely for a straightforward machine learning approach to yield a model that can predict root numbers in polynomial time.
Recommended Citation
Pozdnyakov, Alexey, "Murmurations and Root Numbers" (2024). University Scholar Projects. 95.
https://digitalcommons.lib.uconn.edu/usp_projects/95