On the rational cuspidal divisor class groups of Drinfeld modular curves X0(𝔭r)

Abstract

Let [Formula: see text] be the rational cuspidal divisor class group of the Drinfeld modular curve [Formula: see text] for a prime power level [Formula: see text]. We relate the rational cuspidal divisors of degree 0 on [Formula: see text] with [Formula: see text]-quotients, where [Formula: see text] is the Drinfeld discriminant function. As a result, we are able to determine explicitly the structure of [Formula: see text] for arbitrary prime [Formula: see text] and [Formula: see text].