Existence of primitive polynomials with three coefficients prescribed

Details Existence of primitive polynomials with three coefficients prescribed Existence of primitive polynomials with three coefficients prescribed

2003-05-27

arxiv.org/abs/math/0305383v1

Mathematics

Number Theory

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

Scientific paper

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.

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