9 citations · 17 across the 7 of their papers we have counts for
7 papers
A proof of the Corrected Beiter conjecture
Jia Zhao, Xianke Zhang
We say that a cyclotomic polynomial Φ_{n}(x) has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of Φ_{n}(x…
On the coefficients of the cyclotomic polynomials of order three
Jia Zhao, Xianke Zhang
We say that a cyclotomic polynomial Phi_{n}(x) has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of Phi_{…
Mordell-Weil groups and Selmer groups of two types of elliptic curves
Derong Qiu, Xianke Zhang
Consider elliptic curves where and are prime numbers with . (1) The Selmer groups $ S^{(2)}(E/{\mathbf{Q}}), S^{(ϕ)}(E…
L-series and their 2-adic and 3-adic valuations at s=1 attached to CM elliptic curves
Derong Qiu, Xianke Zhang
series attached to two classical families of elliptic curves with complex multiplications are studied over number fields, formulae for their special values at bound of…
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 of any real quadratic function field to have a cyclic subgro…
Elliptic curves of twin-primes over Gauss field and Diophantine Equations
DeRong Qiu, Xianke Zhang
Let be twin prime numbers with . Consider the elliptic curves E=E_σ: y^2 = x (x+σp)(x+σq) . (σ=\pm 1). E=E_σis also denoted as E_+ or E_- when σ= +1or $-1.Here the M…