Lower Bounds for the Canonical Height on Drinfeld Modules

We use diophantine approximation to bound from below the canonical height on a Drinfeld module. We first give a positive answer to the Lehmer problem in the case of purely inseparable extensions on Drinfeld modules with at least one supersingular prime. We also revisit the CM case, where we improve the estimates already known, and we finally give a bound of polynomial strength in the general case.