Independence of hyperlogarithms over function fields via algebraic combinatorics

Deneufchâtel, Matthieu; Duchamp, Gérard H. E.; Minh, Vincel Hoang Gnoc and Solomon, Allan I. (2011). Independence of hyperlogarithms over function fields via algebraic combinatorics. In: CAI 2011 : 4th conference on algebraic informatics, 21-24 Jun 2011, Hagenberg/Linz, Austria.

DOI: https://doi.org/10.1007/978-3-642-21493-6_8

URL: http://emis.icm.edu.pl/journals/SLC/wpapers/s67vor...

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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