Iwasawa-type asymptotic formula for Taelman class groups of Drinfeld modules

Abstract: The Taelman class groups associated to Drinfeld modules over function fields serve as an analogue of ideal class groups of number fields. In this paper, we establish an analogue of Iwasawa's asymptotic formula for $\mathbb{Z}_p$-extensions in the context of the Taelman class groups. For this purpose, we naturally introduce and investigate Taelman class groups with moduli.