For an elliptic curve E/ℚ, the rank of E(ℚ) equals the order of vanishing of L(E,s) at s=1, and the leading Taylor coefficient has an explicit arithmetic formula. Millennium Prize problem; partial progress by Kolyvagin and others.
For an elliptic curve E/ℚ, the rank of E(ℚ) equals the order of vanishing of L(E,s) at s=1, and the leading Taylor coefficient has an explicit arithmetic formula. Millennium Prize problem; partial progress by Kolyvagin and others.