An optimal multiplicity estimate for interpolation determinants in three logarithms
In the kit of Mignotte and Voutier for linear forms in three logarithms, the order of vanishing at the origin of the interpolation determinant is bounded below by Waldschmidt's general multiplicity lemma; the authors indicate that this estimate should be improvable. We give a lower bound for this order which is optimal for generic points. The functions involved span a space whose initial forms are described by a uniqueness property for a linear differential equation with constant coefficients. As a consequence, the left-hand side of their criterion (2.8) can be taken equal to…
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