An explicit Gross-Zagier formula related to the Sylvester Conjecture

2017/08/17 by Hu, Yueke, Shu, Jie, Yin, Hongbo · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.05266

Abstract

Let p≡ 4,7\mod 9 be a rational prime number such that 3\mod p is not a cubic residue. In this paper we prove the 3-part of the product of the full BSD conjectures for E_p and E_3p³ is true using an explicit Gross-Zagier formula, where E_p: x³+y³=p and E_3p²: x³+y³=3p² are the elliptic curves related to the Sylvester conjecture and cube sum problems.

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