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Sur les séries \(L\) associées aux formes modulaires. (On L-series associated to modular forms). (French) Zbl 0756.11012
The first part of this paper is concerned with theorems like Weil’s on the determination of modular forms for \(\Gamma_ 0(N)\) by functional equations for the \(L\)-series. The author formulates a result in which only a finite number of twists of the \(L\)-series of Dirichlet characters is needed. The second part of the paper is concerned with Manin’s explicit formula for the eigenvalues of Hecke operators. Here an extension of Manin’s result is formulated.
In both cases the author follows the proof given by Weil or by Manin and in both cases he overlooks the existence of Dirichlet characters which are neither primitive nor principal, so that the proofs are incomplete.

MSC:
11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F25 Hecke-Petersson operators, differential operators (one variable)
11F11 Holomorphic modular forms of integral weight
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References:
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