Eisenstein Polynomials over Function Fields

TL;DR

This paper calculates how common Eisenstein polynomials are over function fields, providing insights into their distribution among polynomials with coefficients in certain subrings.

Contribution

It introduces a method to compute the density of Eisenstein polynomials over function fields, extending previous work in number fields to the function field setting.

Findings

Density formulas for Eisenstein polynomials over function fields

Extension of classical results to new algebraic structures

Quantitative measures of polynomial distributions

Abstract

In this paper we compute the density of monic and non-monic Eisenstein polynomials of fixed degree having entries in an integrally closed subring of a function field over a finite field.