Density of Special Classes of Polynomials with Squarefree Discriminant

2025/05/11 by Gian Cordana Sanjaya, Sanjaya, Gian Cordana
Mathematics · #11N32 #11N36 #11T06 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.06820

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the problem of determining the density of monic polynomials over ℤ_p with squarefree discriminant over various subsets of the set of monic polynomials over ℤ_p of fixed degree. We compute the density of polynomials in each subset whose discriminant is squarefree, and we compute the density of polynomials f in each subset such that ℤ_p[x]/(f(x)) is the maximal order of ℚ_p[x]/(f(x)).

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