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 = M S) 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.

International audienceWe investigate the asymptotic behavior of the Selberg-like integral $$ \frac1{N!}\int_{[0,1]^N}x_1^p\prod_{

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In this paper, we explain the importance of finite decomposition semigroups and present two theorems related to their structure.