×

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
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] [EZ] , , The arithmetical function ∑d|n log d/d, Demonstratio Mathematica, vol.VI (1973).
[2] [Hei] , On the average length of a class of continued fractions, Number Theorical Analysis (Papers in honor of Edmund Landau), Plenum, New-York, 1966.
[3] [Man 1] , Parabolic points and zeta functions of modular curves, Math. USSR Izvestija, vol.6, n°1 (1972). · Zbl 0248.14010
[4] Some remarks on the instability flag, Tôhoku Math. Journ. · Zbl 0567.14027
[5] [Man 3] , Periods of parabolic forms and p-adic Hecke series, Math. USSR Sbornik, vol.21, n°3 (1973). · Zbl 0293.14008
[6] [Maz] , Courbes elliptiques et symboles modulaires, Séminaire Bourbaki 24ème année, n°414 (1971/1972). · Zbl 0276.14012
[7] [Shi] , Introduction to the arithmetic theory of automorphic functions, Princeton University Press, 1971. · Zbl 0221.10029
[8] [Sho] , Modular symbols of arbitrary weight, Functional analysis and its applications, vol.10, n°1 (1976).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.