Lehmer problem and Drinfeld modules

We propose a lower bound estimate in Dobrowolski's form of the canonical height of a Drinfeld module having a positive density of supersingular primes. This estimate takes into account the inseparable case and it is given as a function of: the degree of the field of coefficients, the height of the module and its rank. We will show that the class of Drinfeld modules we consider includes all CM Drinfeld modules with rank either 1 or a prime number different from the field characteristic.