Explicit degree bounds for right factors of linear differential operators

Alin Bostan (1) , Tanguy Rivoal (2) , Bruno Salvy (3)

1 SPECFUN - Symbolic Special Functions : Fast and Certified
2 IF - Institut Fourier
3 ARIC - Arithmetic and Computing

If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominators of very high degree. We give a completely explicit bound for the degrees of the (monic) right factors in terms of the degree and the order of the original operator, as well as the largest modulus of the local exponents at all its singularities, for which bounds are known in terms of the degree, the order and the height of the original operator.

Mots clés: Differential operators; Factorization; Fuchs’ relation

Domaines: Analyse classique [math.CA]; Théorie des nombres [math.NT]

Alin Bostan, Tanguy Rivoal, Bruno Salvy. Explicit degree bounds for right factors of linear differential operators. 2019. ⟨hal-02154679v2⟩