四分之一平面上有理系数加权游动的伽罗瓦群的一个上界和判别准则
An upper bound and criteria for the Galois group of weighted walks with rational coefficients in the quarter plane
摘要：
利用Mazur关于椭圆曲线挠率的定理，得到了与四分之一平面$\mathbb{Z}^2_+$中的加权游动相关联的有限伽罗瓦群$\mathcal{H}$的阶的一个上界24.通过简单的几何论证重新导出了$\mathcal{H}$为4阶或6阶的显式判据。利用除法多项式，还得到了阶为$4m$或$4m+2$的$\mathcal{H}$的递归判据.作为推论，给出了$\mathcal{H}$为8阶的显式判据，比现有方法简单得多.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
