Xianke Zhang

collaborators

3 papers

math.NT2001

Mordell-Weil groups and Selmer groups of two types of elliptic curves

Derong Qiu, Xianke Zhang

Consider elliptic curves $E = E_{σ} : y^{2} = x (x + σ p) (x + σ q),$ where $σ = \pm 1,$ $p$ and $q$ are prime numbers with $p + 2 = q$ . (1) The Selmer groups $ S^{(2)}(E/{\mathbf{Q}}), S^{(ϕ)}(E…

math.NT2000

Ideal class groups and subgroups of real quadratic function fields

KunPeng Wang, Xianke Zhang

Here we study algebraic function fields K, give necessary and sufficient condition for the ideal class group $H (K)$ of any real quadratic function field $K$ to have a cyclic subgro…

math.NT1998

Steinitz class of Mordell groups of elliptic curves with complex multiplication

Tong Liu, Xianke Zhang

Let E be an elliptic curve having Complex Multiplication by the full ring O_K of integers of K=Q(\sqrt{-D}), let H=K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil gr…