Arithmetic statistics of Galois groups

TL;DR

This paper introduces a computational framework to statistically analyze Galois characters with finite images, aiding in the characterization of Galois groups and their associated characters.

Contribution

It provides a novel computational approach for the statistical study of Galois characters, enhancing understanding of Galois groups and character equivalences.

Findings

Framework enables statistical analysis of Galois characters.

Characterization of Galois groups using finite image characters.

Establishes criteria for character equivalence in Galois representations.

Abstract

We develop a computational framework for the statistical characterization of Galois characters with finite image, with application to characterizing Galois groups and establishing equivalence of characters of finite images of $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$.