Zhang-Xiong Wang

activity

20152026

most citedCongruent Elliptic Curves with Non-trivial Shafarevich-Tate Groups

11 citations · 11 across the 5 of their papers we have counts for

collaborators

5 papers

math.PR2026

From boundary random walks to Feller's Brownian Motions

Liping Li, Zhangjie Wang

We establish an invariance principle connecting boundary random walks on $N$ with Feller's Brownian motions on $[0, \infty)$ . A Feller's Brownian motion is a Feller process…

math.NT2023

On the quadratic twist of elliptic curves with full $2$ -torsion

Zhangjie Wang, Shenxing Zhang

Let $E : y^{2} = x (x - a^{2}) (x + b^{2})$ be an elliptic curve with full $2$ -torsion group, where $a$ and $b$ are coprime integers and $2 (a^{2} + b^{2})$ is a square. Assume that the $2$ -Selmer group…

math.NT2017

Non-trivial Shafarevich-Tate Groups of Elliptic Curves

Zhangjie Wang

We characterize quadratic twists of $y^{2} = x (x - a^{2}) (x + b^{2})$ with Mordell-Weil groups and $2$ -primary part of Shafarevich-Tate groups being isomorphic to $(\mathb Z/2\mathbb Z)^2$ und…

math.NT2015

Congruent Elliptic Curves with Non-trivial Shafarevich-Tate Groups: Distribution Part

Zhangjie Wang

We study the distribution of a subclass congruent elliptic curve $E^{(n)} : y^{2} = x^{3} - n^{2} x$ , where $n$ is congruent to $1 (mod 8)$ with all prime factors congruent to $1 (mod 4)$ . We pr…

math.NT2015★ 11 cited

Congruent Elliptic Curves with Non-trivial Shafarevich-Tate Groups

Zhangjie Wang

We study a subclass of congruent elliptic curves $E^{(n)} : y^{2} = x^{3} - n^{2} x$ , where $n$ is a positive integer congruent to $1 (mod 8)$ with all prime factors congruent to $1 (mod 4)$ . We…

From boundary random walks to Feller's Brownian Motions

On the quadratic twist of elliptic curves with full 2-torsion

Non-trivial Shafarevich-Tate Groups of Elliptic Curves

Congruent Elliptic Curves with Non-trivial Shafarevich-Tate Groups: Distribution Part

Congruent Elliptic Curves with Non-trivial Shafarevich-Tate Groups

On the quadratic twist of elliptic curves with full $2$ -torsion