An average Chebotarev Density Theorem for generic rank 2 Drinfeld modules with complex multiplication

Abstract

Let q be an odd prime power and let A = F q [ T ] , k = F q ( T ) . Let ψ be a Drinfeld A -module over k , of rank 2 and with a non-trivial endomorphism ring. We prove an average effective Chebotarev Density Theorem for the primes splitting completely in the division fields k ( ψ [ d ] ) of ψ , with a very small error term. We also apply our techniques to study the primes of good reduction for ψ for which the reduced A -module is cyclic.