The rank of an elliptic curve equals the order of vanishing of its L-function at s = 1. A Clay Millennium Prize problem.
4 machine-reviewed papers whose extracted
claims name this problem. Matching is literal, over the claim graph, so every listing traces to
a sentence in a review.
This is the review hub: papers that name the problem, with the machine's
verdict on each. The claims shelf lists the
individual claims themselves, formal (Lean) or stated.
For elliptic curves ordered by height, the first moment of |Sel2(E)| contains a secondary term of order X^{3/4}, with a power-saving error of size O(X^{3/4-1/3804+epsilon}).
Proves that every prime p ≡ 4,7 mod 9 is a sum of two rational cubes, resolving 2/3 of Sylvester's conjecture via BSD progress and the solved Unbounded Denominators Conjecture.
Authors compute Waldspurger's local period integral for newforms in new cases using minimal vectors and a representation theoretic trick, with an example tied to a setting used for the 3-part BSD conjecture.
Visibility theorems imply nontrivial ℓ-torsion in Sha of quadratic twists of elliptic curves with additive reduction at ℓ; for ℓ=3 this yields pairs of curves with identical BSD data and Kodaira symbols but isomorphic Sha groups containing 3-torsion.