On points with algebraically conjugate coordinates close to smooth curves

On distribution of points with algebraically conjugate coordinates in neighborhood of smooth curves

Let φ : R → R be a continuously differentiable function on an interval J ⊂ R and let α = (α1, α2) be a point with algebraically conjugate coordinates such that the minimal polynomial P of α1, α2 is of degree ≤ n and height ≤ Q. Denote by Mn φ (Q, γ, J) the set of such points α such that |φ(α1)− α2| ≤ c1Q −γ . We show that for a real 0 < γ < 1 and any sufficiently large Q there exist positive va...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Efficient elliptic curve cryptosystems

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

The Tangent Cones at Double points of Prym-Canonical Divisors of Curves of genus 7

Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...

A note on the ramification of torsion points lying on curves of genus at least two

Let C be a curve of genus g > 2 defined over the fraction field K of a complete discrete valuation ring R with algebraically closed residue field. Suppose that char(K) = 0 and that the characteristic of the residue field is not 2. Suppose that the Jacobian Jac(C) has semi-stable reduction over R. Embed C in Jac(C) using a K-rational point. We show that the coordinates of the torsion points lyin...