Let ψ be a character of ${\mathbb{Z}}_p$ of order $p^m$, and $f(x)=x^d+\lambda x^e$ be a binomial of degree d with $(d,e)=1$. The determination of the Newton slopes of the L-functions $L_{f,\psi }(s)$ is interesting and still open for general $d,e$ that coprime. If $p\equiv e(\mathrm{mod}d)$ is large enough, an arithmetic polygon $P_{e,d}$ is defined and shown to be the lower bound for the classical ${(\psi (1)-1)}^{a(p-1)}$-adic Newton polygon of $L_{f,\psi }(s)$. In addition, we show they coincide when $e=2$ for large p, hence the Newton slopes of $L_{f,\psi }(s)$ are determined. Combining Ouyang-Zhang's results on $e=d-1$ and $p\equiv d-1(\mathrm{mod}d)$, we conjecture $P_{e,d}$ coincides with ${(\psi (1)-1)}^{a(p-1)}$-adic Newton polygon of $L_{f,\psi }(s)$ for all e if $p\equiv e(\mathrm{mod}d)$ is large enough.

让ψ是一个字符${\mathbb{Z}}_{磷}$ 按顺序 ${磷}^{米}$， 和 $F(X)=X^d+\lambda X^{\mathrm{电子}}$是d 次的二项式，其中$(d,\mathrm{电子})=1$. L函数的牛顿斜率的确定${升}_{F,\psi }(秒)$ 很有趣，仍然对一般人开放 $d,\mathrm{电子}$那个互质。如果$磷\equiv \mathrm{电子}(\mathrm{模组}d)$ 足够大，算术多边形 ${磷}_{\mathrm{电子},d}$ 被定义并显示为经典的下界 ${(\psi (1)-1)}^{\mathrm{一种}(磷-1)}$-adic Newton 多边形 ${升}_{F,\psi }(秒)$. 此外，我们证明它们重合时$\mathrm{电子}=2$对于大p，因此牛顿斜率${升}_{F,\psi }(秒)$被确定。结合欧阳张的结果$\mathrm{电子}=d-1$ 和 $磷\equiv d-1(\mathrm{模组}d)$，我们推测 ${磷}_{\mathrm{电子},d}$ 与 ${(\psi (1)-1)}^{\mathrm{一种}(磷-1)}$-adic Newton 多边形 ${升}_{F,\psi }(秒)$对于所有e if$磷\equiv \mathrm{电子}(\mathrm{模组}d)$ 足够大。