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Journal Articles Mathematics of Computation Year : 2024

Minimization of differential equations and algebraic values of $E$-functions

Abstract

A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential equation of minimal order having this power series as a solution. This problem exists in both homogeneous and inhomogeneous variants; it is distinct from, but related to, the classical problem of factorization of differential operators. Recently, minimization has found applications in Transcendental Number Theory, more specifically in the computation of non-zero algebraic points where Siegel's $E$-functions take algebraic values. We present algorithms and implementations for these questions, and discuss examples and experiments.
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Dates and versions

hal-03771150 , version 1 (07-09-2022)
hal-03771150 , version 2 (18-07-2023)

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Alin Bostan, Tanguy Rivoal, Bruno Salvy. Minimization of differential equations and algebraic values of $E$-functions. Mathematics of Computation, 2024, 93, pp.1427-1472. ⟨10.1090/mcom/3912⟩. ⟨hal-03771150v2⟩
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