Jie Shu

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20172021

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6 papers · 1 filter

math.NT2021

Generalized Birch lemma and the 2-part of the Birch and Swinnerton-Dyer conjecture for certain elliptic curves

Jie Shu, Shuai Zhai

In the present paper, we generalize the celebrated classical lemma of Birch and Heegner on quadratic twists of elliptic curves over $Q$ . We prove the existence of explicit…

math.NT2019

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

Jie Shu, Hongbo Yin

Let $p \equiv 2, 5 mod 9$ be a prime. We prove that both $3 p$ and $3 p^{2}$ are cube sums. We also establish some explicit Gross-Zagier formulae and investigate the 3 part full BSD conj…

math.NT2019

Waldspurger's period integral for newforms

Yueke Hu, Jie Shu, Hongbo Yin

In this paper we discuss Waldspurger's local period integral for newforms in new cases. The main ingredient is the work \cite{HN18} on Waldspurger's period integral using the minim…

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…

math.NT2017

An explicit Gross-Zagier formula related to the Sylvester Conjecture