Factorization of bivariate sparse polynomials
Volume 191 / 2019
Acta Arithmetica 191 (2019), 361-381
MSC: Primary 13P05; Secondary 12Y05.
DOI: 10.4064/aa171219-18-12
Published online: 19 September 2019
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.
