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Title: Factorization of bivariate sparse polynomials
Author: Amoroso, Francesco
Sombra, Martín
Keywords: Polinomis
Àlgebra commutativa
Cossos algebraics
Commutative algebra
Algebraic fields
Issue Date: 19-Sep-2019
Publisher: Instytut Matematyczny Polskiej Akademii Nauk
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.
Note: Versió postprint del document publicat a:
It is part of: Acta Arithmetica, 2019, vol. 191, p. 361-381
Related resource:
ISSN: 0065-1036
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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