Compositio Mathematica

Simultaneous Nonvanishing of Twists of Automorphic L-Functions

P. Michel a1, J. Vanderkam a2 and P. Michel a3
a1 Mathématiques, Université Montpellier II, CC 051, 34095, Montpellier Cedex 05, France. e-mail:
a2 Center for Communications Research, Thanet Road, Princeton, NJ 08540, U.S.A. e-mail:
a3 P.M. is partially supported by NSF Grant DMS-97-2992 and by the Ellentuck fund (by grants to the Institute for Advanced Study) and by the Institut Universitaire de France.

Article author query
michel p   [Google Scholar] 
vanderkam j   [Google Scholar] 
michel p   [Google Scholar] 


Given three distinct primitive complex characters χ123 satisfying some technical conditions, we prove that the triple product of twisted L-functions L(f·χ1,1/2) L(f·χ2,1/2) L(f·χ3,1/2) does not vanish for a positive proportion of weight 2 primitive forms for Γ0(q), when q goes to infinity through the set of prime numbers. This result, together with some variants, implies the existence of quotients of J0(q) of large dimension satisfying the Birch–Swinnerton-Dyer conjecture over cyclic number fields of degree less than 5.

Key Words: automorphic L-functions; central values; mollification.