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Author: William A. Stein
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 $f$ be a newform and $A_f$ the quotient of $J_0(N)$ constructed by Shimura. We prove that, up to a Manin constant and a power of $2$, the denominator of the rational number $L(A_f,1)/\Omega(A_f)$ divides the order of the image of $(0)-(\infty)$ in $A_f(\Q)$. This provides evidence for the Birch and Swinnerton-Dyer conjecture and raises questions about the structure of $A_f(\Q)$.

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