Logarithmic-type and exponential-type hypergeometric functions for function fields
Logarithmic-type and exponential-type hypergeometric functions for function fields
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函数域的对数型和指数型超几何函数
DOI：
10.1016/j.jnt.2021.05.016
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发表时间：
2022
影响因子：
0.7
通讯作者：
Takehiro Hasegawa
中科院分区：
文献类型：
--
作者：
Takehiro Hasegawa
本文提出了函数场的一种新的超几何函数及其下Drinfeld对数稳定的算子，并研究了该超几何函数所满足的方程。作为应用，我们的函数涉及到一个德林菲尔德模的超奇异多项式，一个德林菲尔德模的周期，以及Kochubei的多对数，它们是经典设置中众所周知的事实的函数-场类比。此外，我们将Thakur证明的Carlitz模的结果推广到Drinfeld模的结果。
This article suggests a new hypergeometric function for function fields and a new operator such that the Drinfeld logarithm is stable under it, and studies an equation satisfied by the hypergeometric function. As applications, our function is related to a supersingular polynomial of Drinfeld modules, a period of Drinfeld modules, and the Kochubei's polylogarithm, which are function-field analogues of well-known facts for the classical setting. Moreover, we generalize results for the Carlitz modules proven by Thakur to those for the Drinfeld ones.