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

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

2007-01-13

arxiv.org/abs/math/0701375v1

Mathematics

Number Theory

17 pages, Part of the results was presented at the Polynomials over Finite Fields and Applications workshop at Banff Internati

Scientific paper

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 $p=2,3$.

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