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Dans ce texte, nous déterminons explicitement les idéaux premiers différentiellement stables dans l’anneau des formes quasi-modulaires pour . Les techniques introduites permettent de préciser des résultats de Nesterenko dans [] et [].
Here we characterise, in a complete and explicit way, the relations of algebraic dependence over of complex values of Hecke-Mahler series taken at algebraic points of the multiplicative group , under a technical hypothesis that a certain sub-module of generated by the ’s has rank one (rank one hypothesis). This is the first part of a work, announced in [Pel1], whose main objective is completely to solve a general problem on the algebraic independence of values of these series.
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