Explicit degree bounds for right factors of linear differential operators. Issue 1 (27th July 2020)

• Record Type: Journal Article
• Authors: Bostan, Alin; Rivoal, Tanguy; Salvy, Bruno
• Is Part Of: Bulletin of the London Mathematical Society. Volume 53:Issue 1(2021)
• Page Start: 53
• Page End: 62
• Publication Date: 2020-07-27
• Subjects: 11J81 -- 16S32 -- 34M15 (primary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12396
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominators of very high degrees. When the base field is C, 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 of 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, we get 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.