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Article

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Accepted version

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2019-09-19

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/168802

Factorization of bivariate sparse polynomials

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https://doi.org/10.4064/aa171219-18-12

Abstract

We prove a function field analogue of a conjecture of Schinzel on the factorization of univariate polynomials over the rationals. We derive from it a finiteness theorem for the irreducible factorizations of the bivariate Laurent polynomials in families with a fixed set of complex coefficients and varying exponents. Roughly speaking, this result shows that the truly bivariate irreducible factors of these sparse Laurent polynomials are also sparse. The proofs are based on a variant of the toric Bertini theorem due to Zannier and to Fuchs, Mantova and Zannier.

Subject

Polinomis, Àlgebra commutativa, Cossos algebraics

Subject (English)

Polynomials, Commutative algebra, Algebraic fields

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

AMOROSO, Francesco and SOMBRA, Martín. Factorization of bivariate sparse polynomials. Acta Arithmetica. 2019. Vol. 191, num. 361-381. ISSN 0065-1036. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/168802

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