Abstract
Let A be the polynomial ring over a finite field. We prove that for every element a of a global A -field of finite A -characteristic the set of places P for which a is a primitive root under the Carlitz action possesses a Dirichlet density. We also give a criterion for this density to be positive. This is an analogue of Bilharz’ version of the primitive roots conjecture of Artin, with G m replaced by the Carlitz module.
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