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1 results

  • Simultaneous Nonvanishing of Twists of Automorphic L-Functions

  • P. Michel, J. Vanderkam, P. Michel
  • Journal:
    Compositio Mathematica / Volume 134 / Issue 2 / November 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 135-191
    Print publication:
    November 2002
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  • Given three distinct primitive complex characters χ1,χ2,χ3 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.