Ideaux stables dans certains anneaux differentiels de formes quasi-modulaires de Hilbert
Federico Pellarin
Abstract
Nesterenko proved, among other results, the algebraic independence over of the numbers π,eπ,Γ(1/4). A very important feature of his proof is a multiplicity estimate for quasi-modular forms associated to 2() which involves profound differential properties of certain non-linear differential systems. The aim of this article is to begin the study of the analogous properties for Hilbert modular and quasi-modular forms, especially those which are associated with the number field (5). We show that the differential structure of these functions has several analogies with the differential structure of the quasi-modular forms associated to 2().
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