Irreducible polynomials with prescribed trace and restricted norm
Number Theory
2007-10-16 v1
Abstract
Let GF(q), q=p^r, be a finite field with a primitive element g. In this paper we use exponential sums and Jacobi sums to compute the number of the irreducible polynomials of degree m over GF(q) with trace fixed and norm restricted to a coset of a subgroup <g^s>, s|(q-1). We give the number explicitly for s=2, 3, 4 when q=p, and for s|(p^e+1) when r=2en. Finally, we give explicit formulae for the number when both trace and norm are fixed, p=2 and m =< 30.
Cite
@article{arxiv.0710.2767,
title = {Irreducible polynomials with prescribed trace and restricted norm},
author = {K. Kononen and M. Moisio and M. Rinta-aho and K. Vaananen},
journal= {arXiv preprint arXiv:0710.2767},
year = {2007}
}
Comments
25 pages