论文标题
Galois加权步行组的上限和标准在四分之一平面中具有合理系数
An upper bound and criteria for the Galois group of weighted walks with rational coefficients in the quarter plane
论文作者
论文摘要
使用Mazur定理在椭圆曲线的扭转上，获得了有限的Galois组$ \ Mathcal {H} $的上限24，与四分之一平面$ \ MATHBB {Z}^2 _+$相关的加权步行相关。 $ \ Mathcal {H} $具有4或6的明确标准是通过简单的几何参数重新验证的。还可以获得$ \ Mathcal {H} $的递归标准，其订单$ 4M $或400万美元+2 $。作为推论，给出了订单8的$ \ mathcal {h} $的显式标准，并且比现有方法要简单得多。
Using Mazur's theorem on torsions of elliptic curves, an upper bound 24 for the order of the finite Galois group $\mathcal{H}$ associated with weighted walks in the quarter plane $\mathbb{Z}^2_+$ is obtained. The explicit criterion for $\mathcal{H}$ to have order 4 or 6 is rederived by simple geometric argument. Using division polynomials, a recursive criterion for $\mathcal{H}$ having order $4m$ or $4m+2$ is also obtained. As a corollary, explicit criterion for $\mathcal{H}$ to have order 8 is given and is much simpler than the existing method.
