EXPLICIT SURJECTIVITY RESULTS FOR DRINFELD MODULES OF RANK 2

Let and . Suppose that is a Drinfeld -module of rank over which does not have complex multiplication. We obtain an explicit upper bound (dependent on ) on the degree of primes of such that the image of the Galois representation on the -torsion points of is not surjective, in the case of odd. Our results are a Drinfeld module analogue of Serre’s explicit large image results for the Galois representations on -torsion points of elliptic curves (Serre, Proprietes galoisiennes des points d’ordre fini des courbes elliptiques, Invent. Math. 15 (1972), 259–331; Serre, Quelques applications du theoreme de densite de Chebotarev, Inst. Hautes Etudes Sci. Publ. Math. 54 (1981), 323–401.) and are unconditional because the generalized Riemann hypothesis for function fields holds. An explicit isogeny theorem for Drinfeld -modules of rank over is also proven.