Machine learning for number theory: unsupervised learning with L-functions

Oliver, T. 2024. Machine learning for number theory: unsupervised learning with L-functions. 8th International Congress on Mathematical Software (ICMS2024). Durham University 22 - 25 Jul 2024 Springer. https://doi.org/10.1007/978-3-031-64529-7_21

TitleMachine learning for number theory: unsupervised learning with L-functions
AuthorsOliver, T.
TypeConference paper
Abstract

There is a strong tradition of computation in number theory, with notable data-driven insights including the prime number theorem and the conjecture of Birch and Swinnerton-Dyer.
A huge arithmetic online database known as the LMFDB went live in the mid-2010s, to which we began applying machine learning methodologies in 2020. This led to a data scientific perspective on old problems, and the discovery of surprising new structures in arithmetic statistics known as "murmurations". In this extended abstract, we will apply unsupervised learning techniques to a small dataset taken from the LMFDB, chosen so as to demonstrate one approach to generalising the original experiments.

KeywordsPCA
Clustering
L-functions
Year2024
Conference8th International Congress on Mathematical Software (ICMS2024)
PublisherSpringer
Publication dates
Published online17 Jul 2024
JournalLecture Notes in Computer Science
Journal citation1479, pp. 196-203
ISSN0302-9743
1611-3349
Digital Object Identifier (DOI)https://doi.org/10.1007/978-3-031-64529-7_21
Web address (URL)https://link.springer.com/chapter/10.1007/978-3-031-64529-7_21

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