Surjectivity of the adelic Galois representation associated to a Drinfeld module of rank 3

Notes on Explicit Constructions of Arithmetically Equivalent Global Function Fields via Torsion Points On Drinfeld Modules

“…In addition to that D.Zywina [12] constructed an explicit example of a Drinfeld module of rank two with the surjective Adelic representation. A similar example for rank 3 modules has been recently given in [2]. Those instances could be used to exclude the "probabilistic" part of the algorithm.…”

Exceptional cases of adelic surjectivity for Drinfeld modules of rank 2

“…Zywina [Zyw11] proved the adelic surjectivity for a Drinfeld A-module over F of rank 2 under the assumption that q ≥ 5 is an odd prime power. The author [Che20] proved the adelic surjectivity for a Drinfeld A-module over F of rank 3 under the condition that q = p e is a prime power with p ≥ 5 and q ≡ 1 mod 3.…”