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Opérateurs de Hecke pour \(\Gamma_ 0(N)\) et fractions continues. (Hecke operators for \(\Gamma_ 0(N)\) and continued fractions). (French) Zbl 0727.11020

Nous rappelons que Manin décrit l’homologie singulière relative aux pointes de la courbe modulaire \(X_ 0(N)\) comme un quotient du groupe \({\mathbb{Z}}^{({\mathbb{P}}^ 1({\mathbb{Z}}/N{\mathbb{Z}}))}\). En s’appuyant sur des techniques de fractions continues, nous donnons une expression indépendante de N d’un relèvement de l’action des opérateurs de Hecke de \(H_ 1(X_ 0(N),...,{\mathbb{Z}})\) sur \({\mathbb{Z}}^{({\mathbb{P}}^ 1({\mathbb{Z}}/N{\mathbb{Z}}))}\).
Reviewer: L.Merel (Paris)

MSC:

11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F25 Hecke-Petersson operators, differential operators (one variable)
11F30 Fourier coefficients of automorphic forms
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References:

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