We use Galois theory of difference equations to study the nature of the generating series of (weighted) walks in the quarter plane with genus zero kernel curve. Using this approach, we prove that the generating series do not satisfy any nontrivial (possibly nonlinear) algebraic differential equation with rational coefficients.

中文翻译：

---

走在四分之一平面中：属零情况

我们使用差分方程的Galois理论研究零类核曲线在四分之一平面上生成的（加权）游动序列的性质。使用这种方法，我们证明了生成级数不满足任何具有有理系数的非平凡（可能是非线性）代数微分方程。