Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics

  • Matthieu Deneufchâtel
  • Gérard H. E. Duchamp
  • Vincel Hoang Ngoc Minh
  • Allan I. Solomon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6742)


We obtain a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms. The key fact is that the multiplier (i.e. the factor M in the differential equation dS = MS) has only singularities of first order (Fuchsian-type equations) and this implies that they freely span a space which contains no primitive. We give direct applications where we extend the property of linear independence to the largest known ring of coefficients.


Formal Power Series Linear Independence Operator Calculus Iterate Integral Exponential Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Matthieu Deneufchâtel
    • 1
  • Gérard H. E. Duchamp
    • 1
  • Vincel Hoang Ngoc Minh
    • 1
  • Allan I. Solomon
    • 2
    • 3
  1. 1.Institut Galilée, LIPN - UMR 7030 CNRS - Université Paris 13VilletaneuseFrance
  2. 2.Department of Physics and AstronomyThe Open UniversityMilton KeynesUK
  3. 3.LPTMC - UMR 7600 CNRS - Université Paris 6ParisFrance

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