Counting Drinfeld modules with prescribed local conditions.

We give asymptotics for the number of isomorphism classes of Drinfeld F q [ T ] -modules over F q (T) of a given height, which satisfy prescribed sets of local conditions. This is done by relating our problem to a problem about counting points on weighted projective stacks. Our results for counting points of bounded height on weighted projective stacks over global function fields may be of independent interest. [ABSTRACT FROM AUTHOR]