Density of Special Classes of Polynomials with Squarefree Discriminant

Gian Cordana Sanjaya

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arXiv · 2505.06820

Density of Special Classes of Polynomials with Squarefree Discriminant

Gian Cordana Sanjaya

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Abstract

In this paper, we consider the problem of determining the density of monic polynomials over $\mathbb{Z}_p$ with squarefree discriminant over various subsets of the set of monic polynomials over $\mathbb{Z}_p$ 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 $\mathbb{Z}_p[x]/(f(x))$ is the maximal order of $\mathbb{Q}_p[x]/(f(x))$.

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Gian Cordana Sanjaya. 2025-05-11. Density of Special Classes of Polynomials with Squarefree Discriminant. https://arxiv.org/abs/2505.06820

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