A uniform relative Dobrowolskis lower bound over abelian extensions

A Lower Bound for the Canoni al Height on Ellipti Curves over Abelian Extensions

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

A Lower Bound for the Canonical Height on Elliptic Curves over Abelian Extensions

Let E/K be an elliptic curve defined over a number field, let ĥ be the canonical height on E, and let K/K be the maximal abelian extension of K. Extending work of Baker [4], we prove that there is a constant C(E/K) > 0 so that every nontorsion point P ∈ E(K) satisfies ĥ(P ) > C(E/K).

Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions

Let K be a number field and let E/K be an elliptic curve. If E has complex multiplication, we show that there is a positive lower bound for the canonical height of non-torsion points on E defined over the maximal abelian extension K of K. This is analogous to results of Amoroso-Dvornicich and Amoroso-Zannier for the multiplicative group. We also show that if E has non-integral j-invariant (so t...

On the Ambiguity of Differentially Uniform Functions

Recently, the ambiguity and deficiency of a given bijective mapping F over a finite abelian group G were introduced by Panario et al. [PSS+13, PSSW11] to measure the balancedness of the derivatives DaF (x) = F (x+a)−F (x) for all a ∈ G\{0}. Fundamental properties and cryptographic significance of these measures were further studied in [PSSW11, PSS+13]. In this paper, we extend the study of the ...