论文标题
高转移和线性差方程，指数情况
Hypertranscendence and linear difference equations, the exponential case
论文作者
论文摘要
在本文中，我们研究了$ \ Mathbb {C}（x）$涉及操作员$ρ：y（x）\ mapsto y（x+h）$的$ \ mathbb {c}（x）$系数线性移位差方程的Meromorphic函数解决方案。我们证明，如果$ f $是代数微分方程的解决方案，则$ f $属于用定期功能和指数级制造的环。我们的证明是基于Hardouin和Singer发起的参数化差异理论。
In this paper we study meromorphic functions solutions of linear shift difference equations in coefficients in $\mathbb{C}(x)$ involving the operator $ρ: y(x)\mapsto y(x+h)$, for some $h\in \mathbb{C}^*$. We prove that if $f$ is solution of an algebraic differential equation, then $f$ belongs to a ring that is made with periodic functions and exponentials. Our proof is based on the parametrized difference Galois theory initiated by Hardouin and Singer.
