188 citations · 232 across the 7 of their papers we have counts for
8 papers
Classical Iwasawa theory and infinite descent on a family of abelian varieties
John Coates, Jianing Li, Yongxiong Li
For primes , the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family o…
Non-vanishing theorems for central -values of some elliptic curves with complex multiplication II
John Coates, Yongxiong Li
Let be any prime , , and let be the Hilbert class field of . Let be the Gross elliptic curve defined over with com…
Non-vanishing theorems for central -values of some elliptic curves with complex multiplication
John Coates, Yongxiong Li
The paper uses Iwasawa theory at the prime to prove non-vanishing theorems for the value at of the complex -series of certain quadratic twists of the Gross family of…
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 and…
On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication
John Coates, Minhyong Kim, Zhibin Liang +1
Given an elliptic curve E over Q with complex multiplication having good reduction at 2, we investigate the 2-adic valuation of the algebraic part of the L-value at 1 for a family…
Selmer varieties for curves with CM Jacobians
John Coates, Minhyong Kim
We study the Selmer variety associated to a canonical quotient of the $\Q_p$-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over $\Q$ wh…