Linear Forms in Monic Integer Polynomials

Canadian mathematical bulletin

Art?ras Dubickas¹ 

[1] Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania

关键词: irreducible polynomial;    height;    linear form in polynomials;    Eisenstein's criterion;   

DOI  :  10.4153/CMB-2011-179-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove a necessary and sufficient condition on the list ofnonzero integers $u_1,dots,u_k$, $k geq 2$, under which a monicpolynomial $f in mathbb{Z}[x]$ is expressible by a linear form$u_1f_1+dots+u_kf_k$ in monic polynomials $f_1,dots,f_k inmathbb{Z}[x]$. This condition is independent of $f$. We also show that ifthis condition holds, then the monic polynomials $f_1,dots,f_k$can be chosen to be irreducible in $mathbb{Z}[x]$.

【 授权许可】

Unknown