Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions |
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Authors: | Marc Huttner |
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Institution: | (1) UFR de Mathématiques, UMR AGAT CNRS, Université des Sciences et Technologies de Lille, F-59665 Villeneuve d’Ascq Cedex, France |
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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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