Cube sums of the forms 3p and 3p2 II

Cube sums of the forms 3p and 3p2 II

Let p ≡ 2 , 5 mod 9 be a prime. We prove that both 3 p and 3 p 2 are the sums of two rational cubes. We also establish some explicit Gross–Zagier formulae and investigate the 3-part of the full BSD conjecture of the related elliptic curves.

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Veröffentlicht in:Mathematische annalen 2023, Vol.385 (3-4), p.1037-1060
Hauptverfasser: Shu, Jie, Yin, Hongbo
Format: Artikel
Sprache:eng
Schlagworte:
Cubes
Curves
Mathematics
Mathematics and Statistics
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Zusammenfassung:Let p ≡ 2 , 5 mod 9 be a prime. We prove that both 3 p and 3 p 2 are the sums of two rational cubes. We also establish some explicit Gross–Zagier formulae and investigate the 3-part of the full BSD conjecture of the related elliptic curves.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-022-02370-3