Counting Matrices in SL3(Z) with Fixed Completely Split Character Polynomial: Preliminary Upper Bounds

TL;DR

This paper investigates the enumeration of matrices in SL3(Z) with a specific type of characteristic polynomial that splits completely over the rationals, providing initial upper bounds for their count.

Contribution

It introduces preliminary upper bounds for counting matrices in SL3(Z) with completely split characteristic polynomials over Q.

Findings

Established initial upper bounds for the number of such matrices.

Focused on matrices in SL3(Z) with specific polynomial splitting properties.

Abstract

We count matrices in the special linear group SL(n, Z) whose characteristic polynomials split completely over Q.