2022/09/05 by Alin Bostan, Bostan, Alin, Tanguy Rivoal +3 · 1 citation
Mathematics · #11J81 #16S32 #33F10 #34M15 #68W30 #Algebraic and Geometric Analysis #FOS: Computer and information sciences #FOS: Mathematics #History and Theory of Mathematics #Mathematical Approximation and Integration #Mathematics and Applications #Number Theory (math.NT) #Numerical methods for differential equations #Symbolic Computation (cs.SC) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2209.01827
openalex publication_date 2022/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A power series being given as the solution of a linear differential equation\nwith appropriate initial conditions, minimization consists in finding a\nnon-trivial linear differential equation of minimal order having this power\nseries as a solution. This problem exists in both homogeneous and inhomogeneous\nvariants; it is distinct from, but related to, the classical problem of\nfactorization of differential operators. Recently, minimization has found\napplications in Transcendental Number Theory, more specifically in the\ncomputation of non-zero algebraic points where Siegel's E-functions take\nalgebraic values. We present algorithms and implementations for these\nquestions, and discuss examples and experiments.\n