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Abstract 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… Click to show full abstract
Abstract 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.
Journal Title: Journal of Number Theory
Year Published: 2021
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