Machine Learning Class Numbers of Real Quadratic Fields

TL;DR

This paper applies machine learning techniques to classify real quadratic fields by their class numbers, providing insights into the features influencing class number distinctions and developing predictive formulas.

Contribution

It introduces a data-driven approach to classify real quadratic fields' class numbers and derives machine-learned formulas for this classification.

Findings

Successfully distinguished class numbers with machine learning

Identified key features affecting class number classification

Developed formulas for predicting class numbers

Abstract

We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a data-scientific perspective, apply the methodology of feature analysis and principal component analysis, and use symbolic classification to develop machine-learned formulas for class numbers 1, 2 and 3 that apply to our dataset.