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arXiv · 1903.08441

On some classes of irreducible polynomials

Jaime Gutierrez·Jorge Jimenez Urroz
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Abstract

The aim of the paper is to produce new families of irreducible polynomials, generalizing previous results in the area. One example of our general result is that for a near-separated polynomial, i.e., polynomials of the form $F(x,y)=f_1(x)f_2(y)-f_2(x)f_1(y)$, then $F(x,y)+r$ is always irreducible for any constant $r$ different from zero. We also provide the biggest known family of HIP polynomials in several variables. These are polynomials $p(x_1,\ldots,x_n) \in K[x_1,\ldots,x_n]$ over a zero characteristic field $K$ such that $p(h_1(x_1),\ldots,h_n(x_n))$ is irreducible over $K$ for every $n$-tuple $h_1(x_1),\ldots,h_n(x_n)$ of non constant one variable polynomials over $K$. The results can also be applied to fields of positive characteristic, with some modifications.

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Jaime Gutierrez, Jorge Jimenez Urroz. 2019-03-20. On some classes of irreducible polynomials. https://arxiv.org/abs/1903.08441

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