A note on GL2 converse theorems

A. Diaconu, A. Perelli, A. Zaharescu

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Abstract

Weil's well-known converse theorem shows that modular forms f ∈ Mk0(q)) are characterized by the functional equation for twists of Lf(s). Conrey-Farmer had partial success at replacing the assumption on twists by the assumption of Lf(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 languageEnglish (US)
Pages (from-to)621-624
Number of pages4
JournalComptes Rendus Mathematique
Volume334
Issue number8
DOIs
StatePublished - Apr 30 2002

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