Irreducible Polynomials with Coefficients in an Affine Algebraic Set

Neil Kolekar

Irreducible Polynomials with Coefficients in an Affine Algebraic Set

Number Theory 2025-12-11 v1

Authors: Neil Kolekar

Abstract

In this paper, we give error bounds on the number of monic irreducible polynomials $a_0+a_1x+\dots+a_{n-1}x^{n-1}+x^n$ over a finite field $\mathbb{F}_q$ of degree $n$ with $(a_0, a_1, \dots, a_{n-1}, 1)$ lying in a fixed affine algebraic set $V$ of points in $\mathbb{F}_q^{n+1}$ .

Keywords

polynomials over finite fields polynomial theory polynomial roots

Cite

@article{arxiv.2512.08994,
  title  = {Irreducible Polynomials with Coefficients in an Affine Algebraic Set},
  author = {Neil Kolekar},
  journal= {arXiv preprint arXiv:2512.08994},
  year   = {2025}
}

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