English

Cube sums of form $3p$ and $3p^2$ II

Number Theory 2019-10-01 v1

Abstract

Let p2,5mod9p\equiv 2,5\mod 9 be a prime. We prove that both 3p3p and 3p23p^2 are cube sums. We also establish some explicit Gross-Zagier formulae and investigate the 3 part full BSD conjecture of the related elliptic curves.

Keywords

Cite

@article{arxiv.1909.13800,
  title  = {Cube sums of form $3p$ and $3p^2$ II},
  author = {Jie Shu and Hongbo Yin},
  journal= {arXiv preprint arXiv:1909.13800},
  year   = {2019}
}