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Sur les idéaux stables dans certains anneaux différentiels de formes quasi-modulaires de Hilbert

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Abstract

Nesterenko (Sb. Math. 187:1319–1348, [1996]) proved, among other results, the algebraic independence over ℚ of the numbers π and e π. A very important feature of his proof is a multiplicity estimate for quasi-modular forms associated to SL 2(ℤ) which involves differential properties of certain non-linear differential systems.

The aim of this article is to begin the study of the corresponding properties for Hilbert modular and quasi-modular forms, especially those which are associated with the number field \(\mathbb{Q}(\sqrt{5})\) . We show that the differential structure of these functions has several analogies with the differential structure of the quasi-modular forms associated to SL 2(ℤ).

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  1. LaMUSA, Faculté de Sciences, 23, rue du Docteur Paul Michelon, 42023, Saint-Etienne Cedex 2, France

    Federico Pellarin

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  1. Federico Pellarin
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Correspondence to Federico Pellarin.

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Pellarin, F. Sur les idéaux stables dans certains anneaux différentiels de formes quasi-modulaires de Hilbert. Ramanujan J 15, 147–175 (2008). https://doi.org/10.1007/s11139-007-9069-x

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  • DOI: https://doi.org/10.1007/s11139-007-9069-x

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