Cube Sum Problem and an Explicit Gross-Zagier Formula

Li Cai, Jie Shu, Ye Tian

A nonzero rational number is called a cube sum if it is of form $a^3+b^3$ with $a,b\in {\mathbb{Q}}^{\times }$. In this paper, we prove that for any odd integer $k\ge 1$, there exist i…