Yong-Xiong Li

activity

20132023

most citedNon-vanishing theorems for central

L

-values of some elliptic curves with complex multiplication

7 citations · 10 across the 6 of their papers we have counts for

collaborators

8 papers

math.NT2023

An application of Birch-Tate formula to tame kernels of real quadratic number fields

Li-Tong Deng, Yong-Xiong Li

Let $F$ be a real quadratic number field with discriminant $D$ and $O_{F}$ the ring of integers in $F$ . Let $χ_{F}$ be the Dirichlet character associated to $F / Q$ . W…

math.NT2020

Classical Iwasawa theory and infinite descent on a family of abelian varieties

John Coates, Jianing Li, Yongxiong Li

For primes $q \equiv 7 mod 16$ , the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family o…

math.NT2019★ 1 cited

A classical family of elliptic curves having rank one and the $2$ -primary part of their Tate-Shafarevich group non-trivial

Yukako Kezuka, Yongxiong Li

We study elliptic curves of the form $x^{3} + y^{3} = 2 p$ and $x^{3} + y^{3} = 2 p^{2}$ where $p$ is any odd prime satisfying $p \equiv 2 mod 9$ or $p \equiv 5 mod 9$ . We first show that the $3$ -part…

math.NT2019★ 1 cited

Non-vanishing theorems for central $L$ -values of some elliptic curves with complex multiplication II

John Coates, Yongxiong Li

Let $q$ be any prime $\equiv 7 mod 16$ , $K = Q (- q)$ , and let $H$ be the Hilbert class field of $K$ . Let $A / H$ be the Gross elliptic curve defined over $H$ with com…

math.NT2018★ 7 cited

Non-vanishing theorems for central $L$ -values of some elliptic curves with complex multiplication

John Coates, Yongxiong Li

The paper uses Iwasawa theory at the prime $p = 2$ to prove non-vanishing theorems for the value at $s = 1$ of the complex $L$ -series of certain quadratic twists of the Gross family of…

math.NT2017

Analogues of Iwasawa's $μ = 0$ conjecture and the weak Leopoldt conjecture for a non-cyclotomic $Z_{2}$ -extension

Junhwa Choi, Yukako Kezuka, Yongxiong Li

Let $K = Q (- q)$ , where $q$ is any prime number congruent to $7$ modulo $8$ , and let $O$ be the ring of integers of $K$ . The prime $2$ splits in $K$ , say $…

math.NT2016★ 1 cited

On The Birch and Swinnerton-Dyer Conjecture for CM Elliptic Curves over $\BQ$

Yongxiong Li, Yu Liu, Ye Tian

For CM elliptic curve over rational field with analytic rank one, for any potential good ordinary prime p, not dividing the number of roots of unity in the complex multiplication f…

math.NT2013

Quadratic Twists of Elliptic Curves

John Coates, Yongxiong Li, Ye Tian +1

In this paper, we show that Tian's induction method can be generalised to study the Birch-Swinnerton-Dyer conjecture for the quadratic twists, both with global root number $+ 1$ and…

An application of Birch-Tate formula to tame kernels of real quadratic number fields

Classical Iwasawa theory and infinite descent on a family of abelian varieties

A classical family of elliptic curves having rank one and the 2-primary part of their Tate-Shafarevich group non-trivial

Non-vanishing theorems for central L-values of some elliptic curves with complex multiplication II

Non-vanishing theorems for central L-values of some elliptic curves with complex multiplication