Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields

Details Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields

2008-11-24

arxiv.org/abs/0811.3986v1

Mathematics

Number Theory

33 pages

Scientific paper

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the {\em vector degree}, are considered. We show that the number of irreducibles can be computed recursively by degree and that the number of relatively prime pairs can be expressed in terms of the number of irreducibles. We also obtain asymptotic formulas for the number of irreducibles and the number of relatively prime pairs. The asymptotic formulas for the number of irreducibles generalize and improve several previous results by Carlitz, Cohen and Bodin.

Affiliated with

Also associated with

No associations

Rating

Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-303702