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 Af the quotient
of J0(N) constructed by Shimura.
We prove that, up to a Manin constant and a power of 2,
the denominator of the rational number L(Af,1)/Ω(Af)
divides the order of the image of (0)−(∞) in .
This provides evidence for the Birch and Swinnerton-Dyer
conjecture and raises questions about the structure of .