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We give asymptotics for the number of Drinfeld $\mathbb{F}_q[T]$-modules over$\mathbb{F}_q(T)$ of a given height, which satisfy prescribed sets of localconditions. This is done by relating our problem to a problem about countingpoints on weighted projective spaces. Our results for counting points ofbounded height on weighted projective spaces over global function fields may beof independent interest.

Counting Drinfeld modules with prescribed local conditions