TY - JOUR

T1 - A note on GL2 converse theorems

AU - Diaconu, A.

AU - Perelli, A.

AU - Zaharescu, A.

PY - 2002/4/30

Y1 - 2002/4/30

N2 - Weil's well-known converse theorem shows that modular forms f ∈ Mk(Γ0(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.

AB - Weil's well-known converse theorem shows that modular forms f ∈ Mk(Γ0(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.

UR - http://www.scopus.com/inward/record.url?scp=0038392274&partnerID=8YFLogxK

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U2 - 10.1016/S1631-073X(02)02277-X

DO - 10.1016/S1631-073X(02)02277-X

M3 - Article

AN - SCOPUS:0038392274

VL - 334

SP - 621

EP - 624

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 8

ER -