The Birch and Swinnerton-Dyer conjecture for Q-curves
نویسنده
چکیده
Let N ≡ 1(mod 4) be a positive integer and let be the single even primitive quadratic Dirichlet character on (Z/NZ)×. Let f ∈ S2(Γ0(N), ) be a newform with nebentypus . By the Shimura construction, f corresponds to an abelian variety Af defined over Q whose dimension is [Kf : Q] where Kf is the number field associated with f . When dimAf = 2, the Fricke involution wN acts on Af and is defined over Q( √ N), inducing a decomposition
منابع مشابه
Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves
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