Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

M. Moisio; K. Ranto

Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

Number Theory 2007-05-23 v1 Combinatorics

Authors: M. Moisio , K. Ranto

Abstract

Let $F_q$ be a finite field of characteristic $p=2,3$ . We give the number of irreducible polynomials $x^m+a_{m-1}x^{m-1}+...+a_0\in\F_q[x]$ with $a_{m-1}$ and $a_{m-3}$ prescribed for any given $m$ if $p=2$ , and with $a_{m-1}$ and $a_1$ prescribed for $m=1,...,10$ if $p=2,3$ .

Keywords

elliptic curves irreducible polynomials finite fields prescribed coefficients explicit enumeration

Cite

@article{arxiv.math/0701375,
  title  = {Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed},
  author = {M. Moisio and K. Ranto},
  journal= {arXiv preprint arXiv:math/0701375},
  year   = {2007}
}

Comments

17 pages, Part of the results was presented at the Polynomials over Finite Fields and Applications workshop at Banff International Research Station, Canada

Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

Abstract

Keywords

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