Geodesic
Factorization of bivariate sparse polynomials
Francesco Amoroso 1   ; Martín Sombra 2
1 Laboratoire de mathématiques Nicolas Oresme CNRS UMR 6139 Université de Caen BP 5186, 14032 Caen Cedex, France
2 Institució Catalana de Recerca i Estudis Avançats (ICREA) Passeig Lluís Companys~23 08010 Barcelona, Spain and Departament de Matemàtiques i Informàtica Universitat de Barcelona (UB) Gran Via 585 08007 Barcelona, Spain
Acta Arithmetica, Tome 191 (2019) no. 4, pp. 361-381 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa171219-18-12
Keywords: prove function field analogue conjecture schinzel factorization univariate polynomials rationals derive finiteness theorem irreducible factorizations bivariate laurent polynomials families fixed set complex coefficients varying exponents roughly speaking result shows truly bivariate irreducible factors these sparse laurent polynomials sparse proofs based variant toric bertini theorem due zannier fuchs mantova zannier

Francesco Amoroso  1   ; Martín Sombra  2

1 Laboratoire de mathématiques Nicolas Oresme CNRS UMR 6139 Université de Caen BP 5186, 14032 Caen Cedex, France
2 Institució Catalana de Recerca i Estudis Avançats (ICREA) Passeig Lluís Companys~23 08010 Barcelona, Spain and Departament de Matemàtiques i Informàtica Universitat de Barcelona (UB) Gran Via 585 08007 Barcelona, Spain 
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Francesco Amoroso; Martín Sombra. Factorization of bivariate sparse polynomials. Acta Arithmetica, Tome 191 (2019) no. 4, pp. 361-381. doi: 10.4064/aa171219-18-12

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