Square-free smooth polynomials in residue classes and generators of irreducible polynomials

Christian Bagshaw

Square-free smooth polynomials in residue classes and generators of irreducible polynomials

Number Theory 2022-01-28 v2

Authors: Christian Bagshaw

Abstract

Building upon the work of A. Booker and C. Pomerance (2017), we prove that for a prime power $q \geq 7$ , every residue class modulo an irreducible polynomial $F \in \mathbb{F}_q[X]$ has a non-constant, square-free representative which has no irreducible factors of degree exceeding $\text{deg}~F -1$ . We also give applications to generating sequences of irreducible polynomials.

Keywords

square-free polynomials smooth polynomials residue classes irreducible polynomials finite fields

Cite

@article{arxiv.2201.06663,
  title  = {Square-free smooth polynomials in residue classes and generators of irreducible polynomials},
  author = {Christian Bagshaw},
  journal= {arXiv preprint arXiv:2201.06663},
  year   = {2022}
}

Comments

Updated after discovering a typo in a cited paper

Square-free smooth polynomials in residue classes and generators of irreducible polynomials

Abstract

Keywords

Cite

Comments

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