论文标题
P-ADIC不完整的伽马功能和Artin-Hasse型系列
P-adic incomplete gamma functions and Artin-Hasse-type series
论文作者
论文摘要
我们定义和研究与Morita的$ p $ -Adic伽马功能有关的不完整伽马功能的$ P $ ADIC类似物。我们还讨论了与Artin-Hasse系列有关的组合身份，这是组合学指数原理的特殊情况。由此，我们使用$ | | \ m atrm {hom}（g，s_n）的奇怪$ p $ - adic属性，用于拓扑结构生成的组$ g $，使用$ p $ -adic连续性的某些功能的特征$ f \ colon \ colon \ colon \ colon \ mathbb z _ {> 0} \ 0} \ to to mathb $ mathb $ $ c：最后，我们介绍了Artin-Hasse系列的某些标准属性。
We define and study a $p$-adic analogue of the incomplete gamma function related to Morita's $p$-adic gamma function. We also discuss a combinatorial identity related to the Artin-Hasse series, which is a special case of the exponential principle in combinatorics. From this we deduce a curious $p$-adic property of $|\mathrm{Hom} (G,S_n)|$ for a topologically finitely generated group $G$, using a characterization of $p$-adic continuity for certain functions $f \colon \mathbb Z_{>0} \to \mathbb Q_p$ due to O'Desky-Richman. In the end, we give an exposition of some standard properties of the Artin-Hasse series.
