Jie Shu

activity

20172021

collaborators

Showing 2018Show all

2 papers · 1 filter

math.NT2018

Root numbers and Selmer groups for the Jacobian varieties of Fermat curves

Jie Shu

Let $p$ be an odd prime number. Let $K$ be the $p$ -th cyclotomic field and $F$ its maximal real subfield. We give general formulae of the root numbers of the Jacobian varieties of…

math.NT2018

Cube sums of form $3 p$ and $3 p^{2}$

Jie Shu, Xu Song, Hongbo Yin

Let $p \equiv 2, 5 mod 9$ be an odd prime. In this paper, we prove that at least one of $3 p$ and $3 p^{2}$ is a cube sum by constructing certain nontrivial Heegner points. We also estab…

Root numbers and Selmer groups for the Jacobian varieties of Fermat curves

Cube sums of form 3p and 3p2

Cube sums of form $3 p$ and $3 p^{2}$