Abstract :
Letk=imageq(T),k∞=imageq((1/T)), and let us denote byCthe completion of an algebraic closure ofk∞(for the 1/T-adic valuation), and byKsubset ofCa finite extension ofkof degreeD. Let (imagea, Φi) (1less-than-or-equals, slantiless-than-or-equals, slantn) benDrinfeld modules of rank greater-or-equal, slanted1 defined overK(with exponentialseΦi), letu1, …, unset membership, variantCbe such thateΦi(ui)set membership, variantK(1less-than-or-equals, slantiless-than-or-equals, slantn), and letβ0, …, βnben+1 elements ofK. We obtain in this paper a lower bound for the linear form of logarithmsβ0+β1u1+…+βnun(when it is not zero) as a function of the degreeD, the heights of the pointsβi, the absolute values ui and the heights of theeΦi(ui), and the heights of the modules (imagea, Φi).
