Ideaux stables dans certains anneaux differentiels de formes quasi-modulaires de Hilbert

DOI10.1007/S11139-007-9069-XarXivmath/0407381MaRDI QIDQ6474283

F. Pellarin

Publication date: 22 July 2004

Abstract: Nesterenko proved, among other results, the algebraic independence over $QQ$ of the numbers $pi,e^{pi},Gamma(1/4)$. A very important feature of his proof is a multiplicity estimate for quasi-modular forms associated to $$ which involves profound differential properties of certain non-linear differential systems. The aim of this article is to begin the study of the analogous properties for Hilbert modular and quasi-modular forms, especially those which are associated with the number field $QQ(sqrt5)$. We show that the differential structure of these functions has several analogies with the differential structure of the quasi-modular forms associated to $$.

Mathematics Subject Classification ID

Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Hecke-Petersson operators, differential operators (several variables) (11F60)

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