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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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Minimization of differential equations and algebraic values of $E$-functions
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by Alin Bostan, Tanguy Rivoal and Bruno Salvy;
Math. Comp. 93 (2024), 1427-1472
DOI: https://doi.org/10.1090/mcom/3912
Published electronically: October 23, 2023

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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Bibliographic Information
  • Alin Bostan
  • Affiliation: Inria, Université Paris-Saclay, 1 rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
  • MR Author ID: 725685
  • ORCID: 0000-0003-3798-9281
  • Email: alin.bostan@inria.fr
  • Tanguy Rivoal
  • Affiliation: Institut Fourier, CNRS et Université Grenoble Alpes, CS 40700, 38058 Grenoble cedex 9, France
  • MR Author ID: 668668
  • Email: tanguy.rivoal@univ-grenoble-alpes.fr
  • Bruno Salvy
  • Affiliation: Univ Lyon, EnsL, UCBL, CNRS, Inria, LIP, F-69342, LYON Cedex 07, France
  • MR Author ID: 273775
  • ORCID: 0000-0002-4313-0679
  • Email: bruno.salvy@inria.fr
  • Received by editor(s): September 15, 2022
  • Received by editor(s) in revised form: July 17, 2023
  • Published electronically: October 23, 2023
  • Additional Notes: This work was supported by the French ANR grant DeRerumNatura, ANR-19-CE40-0018
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 93 (2024), 1427-1472
  • MSC (2020): Primary 68W30, 11J81, 16S32, 34M15, 33F10
  • DOI: https://doi.org/10.1090/mcom/3912
  • MathSciNet review: 4709207