Abstract
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.
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Deneufchâtel, M., Duchamp, G.H.E., Hoang Ngoc Minh, V., Solomon, A.I. (2011). Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics. In: Winkler, F. (eds) Algebraic Informatics. CAI 2011. Lecture Notes in Computer Science, vol 6742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21493-6_8
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DOI: https://doi.org/10.1007/978-3-642-21493-6_8
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