## Abstract

Weil's well-known converse theorem shows that modular forms f ∈ M_{k}(Γ_{0}(q)) are characterized by the functional equation for twists of L_{f}(s). Conrey-Farmer had partial success at replacing the assumption on twists by the assumption of L_{f}(s) having an Euler product of the appropriate form. In this Note we obtain a hybrid version of Weil's and Conrey-Farmer's results, by proving a converse theorem for all q ≥ 1 under the assumption of the Euler product and, moreover, of the functional equation for the twists to a single modulus.

Original language | English (US) |
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Pages (from-to) | 621-624 |

Number of pages | 4 |

Journal | Comptes Rendus Mathematique |

Volume | 334 |

Issue number | 8 |

DOIs | |

State | Published - Apr 30 2002 |

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