Squarefree discriminants of polynomials with prime coefficients

Valentio Iverson; Gian Cordana Sanjaya; Xiaoheng Wang

Squarefree discriminants of polynomials with prime coefficients

Number Theory 2025-01-28 v2

Authors: Valentio Iverson , Gian Cordana Sanjaya , Xiaoheng Wang

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 $\mathbb{Q}[x]/(f(x))$ .

Keywords

squarefree discriminant monic polynomials prime coefficients maximal order number theory

Cite

@article{arxiv.2501.09697,
  title  = {Squarefree discriminants of polynomials with prime coefficients},
  author = {Valentio Iverson and Gian Cordana Sanjaya and Xiaoheng Wang},
  journal= {arXiv preprint arXiv:2501.09697},
  year   = {2025}
}

Squarefree discriminants of polynomials with prime coefficients

Abstract

Keywords

Cite

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