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The Denominator of the Special Value L(A<sub>f</sub>,1)/Omega(A<sub>f</sub>)

The Denominator of the Special Value L(Af,1)/Omega(Af)

Amod Agashe and William Stein

Let ff be a newform and AfA_f the quotient of J0(N)J_0(N) constructed by Shimura. We prove that, up to a Manin constant and a power of 22, the denominator of the rational number L(Af,1)/Ω(Af)L(A_f,1)/\Omega(A_f) divides the order of the image of (0)()(0)-(\infty) in . This provides evidence for the Birch and Swinnerton-Dyer conjecture and raises questions about the structure of .

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