English

Existence of primitive polynomials with three coefficients prescribed

Number Theory 2007-05-23 v1

Abstract

We demonstrate, using character sum arguments, the existence of primitive polynomials of degree n over a finite field GF(q) with the coefficients for x^(n-1), x^(n-2), and x^(n-3) prescribed, so long as char(GF(q)) is at least 5 and n is at least 9. The cases n=7, 8 are also considered.

Keywords

Cite

@article{arxiv.math/0305383,
  title  = {Existence of primitive polynomials with three coefficients prescribed},
  author = {Donald Mills},
  journal= {arXiv preprint arXiv:math/0305383},
  year   = {2007}
}

Comments

15 pages, 17 tables; see also http://www.math.siu.edu/mills/default1.htm

R2 v1 2026-07-22T16:54:53.740Z