In the 1970s, Dwork defined the logarithmic growth (log-growth for short) filtrations for $p$-adic differential equations $Dx=0$ on the $p$-adic open unit disc $|t|<1$, which measure the asymptotic behavior of solutions $x$ as $|t|\to 1^{-}$. Then, Dwork calculated the log-growth filtration for $p$-adic Gaussian hypergeometric differential equation. In the late 2000s, Chiarellotto and Tsuzuki proposed a fundamental conjecture on the log-growth filtrations for $(\varphi ,\nabla )$-modules over $K[\![t]\!]_0$, which can be regarded as a generalization of Dwork's calculation. In this paper, we prove a generalization of the conjecture to $(\varphi ,\nabla )$-modules over the bounded Robba ring. As an application, we prove a generalization of Dwork's conjecture proposed by Chiarellotto and Tsuzuki on the specialization property for log-growth Newton polygons.

在20世纪70年代，Dwork定义的对数生长（对数生长的简称）的过滤为$ P $进制微分方程$ DX = 0 $在$ P $进制开放单元盘状$ | T | <1 $，该措施解$x$的渐近行为为$|t|\to 1^{-}$。然后，Dwork 计算了$p$ -adic 高斯超几何微分方程的对数增长过滤。在 2000 年代后期，Chiarellotto 和 Tsuzuki 提出了一个关于$(\varphi ,\nabla )$ -modules over $K[\![t]\!]_0$ 的对数增长过滤的基本猜想，可以看作是 Dwork 计算的推广。在本文中，我们证明了对有界 Robba 环上$(\varphi ,\nabla )$ -modules的猜想的推广。作为应用，我们证明了由 Chiarelloto 和 Tsuzuki 提出的关于对数增长牛顿多边形的特化性质的 Dwork 猜想的推广。