Explicit Upper Bound for the (Analytic) Rank of J0(q)

نویسنده

  • E. Kowalski
چکیده

We refine the techniques of our previous paper [KM1] to prove that the average order of vanishing of L-functions of primitive automorphic forms of weight 2 and prime level q satisfies ∑ f∈S2(q)∗ ords= 1 2 L(f, s) ≤ C|S2(q) ∗| with C = 6.5, for all q large enough. On the Birch and Swinnerton-Dyer conjecture, this implies rank J0(q) ≤ C dim J0(q) for q prime large enough.

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تاریخ انتشار 2008