an:05256315
Zbl 1143.34057
Huttner, Marc
Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions
EN
Isr. J. Math. 153, 1-43 (2006).
00211930
2006
j
34M35 30E10 33B30
Fuchsian linear differential equations
The paper is concerned with rational approximations to solutions of certain Fuchsian linear differential equations defined on the Riemann sphere from the viewpoint of the theory of moduli of differential equations with a fixed monodromy group. The author finds a connection between Fuchsian ODE's and Diophantine approximations of special Siegel \(G\)-functions. In particular, the rigidity assumption for the Fuchsian ODE's enables the author to give new explicit formulae for Pad?? approximations.
Yuefei Wang (Beijing)