23 citations · 47 across the 18 of their papers we have counts for
14 papers · 1 filter
Iwasawa invariants and class number parity of multi-quadratic number fields
Qinhao Li, Derong Qiu
In this paper, based mainly on the method of Iwasawa and Kida, by studying in detail the Hasse's unit index and the ramifications of prime ideals, we obtain explicit results of Iwa…
On Rationality of Cubic and Quartic Number Fields
Hang Li, Derong Qiu
In this paper, a new criterion is given to determine the rationality of some complex cubic number fields in terms of divisibility of certain terms of a third-order recurre…
On Twists of A Family of Elliptic Curves and Their Function
Derong Qiu
Let be an elliptic curve defined over a number field, the conjecture of Birch and Swinnerton-Dyer (BSD, for short) asserts a deep relation between the group of ratio…
On cohomology groups of modules of finite type over cyclic groups
Derong Qiu
Let be a cyclic group, in this paper, we study the Herbrand quotient and th cohomology group on finitely generated modules in some cases. When is of order $ 2…
A note on of Hecke series associated to the elliptic curves with CM by
Derong Qiu
Consider elliptic curves defined over the quadratic field $\ \Q(\sqrt{-3}) $. Hecke series attached to are studied, formulae for their valu…
On quadratic twists of elliptic curves and some applications of a refined version of Yu's formula
Derong Qiu
In this paper, we study some cohomology groups and quadratic twists of elliptic curves, and apply Tate local duality and the results of Kramer-Tunnell on local norm cokernel to giv…
A graphical method to calculate Selmer groups of several families of non-CM elliptic curves
Fei Li, Derong Qiu
In this paper, we extend the ideas of Feng [F1], Feng-Xiong [FX] and Faulkner-James [FJ] to calculate the Selmer groups of elliptic curves $ y^{2} = x (x + \varepsilon p D) (x + εq…
On Some Additive Properties of Multiplicative Subsemigroups of Semirings and Arithmetic Applications I
Derong Qiu
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of…
On some congruence properties of elliptic curves
Derong Qiu
In this paper, as a result of a theorem of Serre on congruence properties, a complete solution is given for an open question (see the text) presented recently by Kim, Koo and Park.…
On Some Diophantine Parameters of the Cyclic Torsion Subgroups of Odd Order of Elliptic Curves over
Derong Qiu
In this paper, we give some explicit Diophantine parameters of the cyclic torsion subgroups of odd order of elliptic curves over .
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…
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…
Explicit classification for torsion subgroups of rational points of elliptic curves
Derong Qiu, Xianke Zhang
The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classificatio…