We study the $p$-adic (generalized) hypergeometric equations by using the theory of multiplicative convolution of arithmetic $\mathscr{D}$-modules. As a result, we prove that the hypergeometric isocrystals with suitable rational parameters have a structure of overconvergent $F$-isocrystals.

中文翻译：

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$p$-adic 从算术角度看的广义超几何方程 $\scr{D}$-modules}$

我们通过使用算术 $\mathscr{D}$-modules 的乘法卷积理论研究 $p$-adic（广义）超几何方程。结果，我们证明了具有合适有理参数的超几何同晶具有过收敛的$F$-同晶结构。