Independence of hyperlogarithms over function fields via algebraic combinatorics
Combinatorics
2017-01-24 v3 Symbolic Computation
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 in the differential equation ) 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.
Cite
@article{arxiv.1101.4497,
title = {Independence of hyperlogarithms over function fields via algebraic combinatorics},
author = {Matthieu Deneufchâtel and Gérard Henry Edmond Duchamp and Vincel Hoang Ngoc Minh and Allan I. Solomon},
journal= {arXiv preprint arXiv:1101.4497},
year = {2017}
}