Lower bounds of heights of points on hypersurfaces

) >exp(1/2400) = 1.00041...This result was applied by Schlickewei [Schl] to estimating numbers of solutions of three termS-unit equations in a strikingly successful way. Although very useful, the derivation of theSchlickewei-Wirsing result did not look optimal. It is the goal of this paper to remedy thissituation and also give a generalisation which encompasses the previous results. We finish theintroduction by giving a description of our general setup and main result.Consider a hypersurface Sof multidegree d