用代数组合学证明函数域上超代数的独立性
Independence of hyperlogarithms over function fields via algebraic combinatorics
摘要：
得到了超代数微分方程解线性无关的一个充要条件。关键的事实是乘数（即微分方程$dS=MS$中的因子$M$）只有一阶奇点（Fuchsian型方程），这意味着它们自由地跨越一个不包含本原的空间。我们给直接的应用程序，我们扩展的线性独立性的最大已知环的系数。
英文摘要：
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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