FACTORIZATION OF SPARSE POLYNOMIALS OVER A FUNCTION FIELD

Francesco Amoroso (1) , Martín Sombra (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 UNIROUEN - Université de Rouen Normandie

We present a structure theorem for the non-constant irreducible factors appearing in the family of of all univariate polynomials with a given set of coefficients in a function field and varying exponents. Roughly speaking, this result shows that the non-constant irreducible irreducible factors of these sparse polynomial, are also sparse. This result is based on a refinement of Zannier's toric Bertini theorem.

Domaines: Théorie des nombres [math.NT]

Francesco Amoroso, Martín Sombra. FACTORIZATION OF SPARSE POLYNOMIALS OVER A FUNCTION FIELD. 2016. ⟨hal-01389696v1⟩