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Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions

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Abstract

The aim of this paper is to investigate rational approximations to solutions of some linear Fuchsian differential equations from the perspective of moduli of linear differential equations with fixed monodromy group. One of the main arithmetic applications concerns the study of linear forms involving polylogarithmic functions. In particular, we give an explanation of the well-poised hypergeometric origin of Rivoal’s construction on linear forms involving odd zeta values.

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Authors and Affiliations

  1. UFR de Mathématiques, UMR AGAT CNRS, Université des Sciences et Technologies de Lille, F-59665, Villeneuve d’Ascq Cedex, France

    Marc Huttner

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  1. Marc Huttner
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Correspondence to Marc Huttner.

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Huttner, M. Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions. Isr. J. Math. 153, 1–43 (2006). https://doi.org/10.1007/BF02771777

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  • DOI: https://doi.org/10.1007/BF02771777

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