Section: New Results

Explicit degree bounds for right factors of linear differential operators

If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominators of very high degree. When the base field is $ℂ$, Alin Bostan together with Bruno Salvy (Inria and ENS Lyon) and Tanguy Rivoal (CNRS and U. Grenoble) gave in [13] 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. As a consequence, if a differential operator $L$ has rational function coefficients over a number field, they obtained degree bounds for its monic right factors in terms of the degree, the order and the height of $L$, and of the degree of the number field.