Squarefree discriminants of polynomials with prime coefficients

Valentio Iverson; Gian Cordana Sanjaya; Xiaoheng Wang

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arXiv · 2501.09697

Squarefree discriminants of polynomials with prime coefficients

Valentio Iverson·Gian Cordana Sanjaya·Xiaoheng Wang

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Abstract

In this paper, we consider the family of monic polynomials with prime coefficients and the family of all polynomials with prime coefficients. We determine the number of $f(x)$ in each of these families having: squarefree discriminant; $\mathbb{Z}[x]/(f(x))$ as the maximal order in $\mathbb{Q}[x]/(f(x))$.

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Valentio Iverson, Gian Cordana Sanjaya, Xiaoheng Wang. 2025-01-16. Squarefree discriminants of polynomials with prime coefficients. https://arxiv.org/abs/2501.09697

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