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arXiv · 2402.02324

Some factorization results for bivariate polynomials

Nicolae Ciprian Bonciocat·Rishu Garg·Jitender Singh
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Abstract

We provide upper bounds on the total number of irreducible factors, and in particular irreducibility criteria for some classes of bivariate polynomials $f(x,y)$ over an arbitrary field $\mathbb{K}$. Our results rely on information on the degrees of the coefficients of $f$, and on information on the factorization of the constant term and of the leading coefficient of $f$, viewed as a polynomial in $y$ with coefficients in $\mathbb{K}[x]$. In particular, we provide a generalization of the bivariate version of Perron's irreducibility criterion, and similar results for polynomials in an arbitrary number of indeterminates. The proofs use non-Archimedean absolute values, that are suitable for finding information on the location of the roots of $f$ in an algebraic closure of $\mathbb{K}(x)$.

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Nicolae Ciprian Bonciocat, Rishu Garg, Jitender Singh. 2024-02-04. Some factorization results for bivariate polynomials. https://doi.org/10.1080/00927872.2024.2377390

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