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.
[BCP97] Wieb Bosma, John Cannon, and Catherine Playoust
4 Pith papers cite this work. Polarity classification is still indexing.
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Framework gives conjectural characterization of geometric families of abelian varieties with unbounded average l-Selmer sizes, proven correct when l-torsion module is constant across the family.
For any number field K and genus g ≥ 2, there are infinitely many non-isomorphic hyperelliptic curves over K with Jacobian rank 0, 1, or 2 over K; explicit higher-rank ranges are given for small genera over Q.
Proves explicit Gross-Zagier formula linking CM point heights on E_{p^i} to L-function derivatives for the 4,7 cases of Sylvester's conjecture.
citing papers explorer
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A proof of the $4,7$ cases of Sylvester's conjecture on cube sums
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.
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Tamagawa ratios and unbounded Selmer moments
Framework gives conjectural characterization of geometric families of abelian varieties with unbounded average l-Selmer sizes, proven correct when l-torsion module is constant across the family.
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Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two
For any number field K and genus g ≥ 2, there are infinitely many non-isomorphic hyperelliptic curves over K with Jacobian rank 0, 1, or 2 over K; explicit higher-rank ranges are given for small genera over Q.
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Gross-Zagier formula for the $4, 7$ cases of Sylvester's conjecture
Proves explicit Gross-Zagier formula linking CM point heights on E_{p^i} to L-function derivatives for the 4,7 cases of Sylvester's conjecture.