中文

椭圆曲线与两个系数指定的不可约多项式的显式计数

数论 2007-05-23 v1 组合数学

摘要

FqF_q 为特征 p=2,3p=2,3 的有限域。对于 p=2p=2,我们给出任意给定 mm 时系数 am1a_{m-1}am3a_{m-3} 指定的不可约多项式 xm+am1xm1+...+a0\Fq[x]x^m+a_{m-1}x^{m-1}+...+a_0\in\F_q[x] 的个数;对于 p=2,3p=2,3,我们给出 m=1,...,10m=1,...,10 时系数 am1a_{m-1}a1a_1 指定的此类多项式的个数。

关键词

引用

@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}
}

备注

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