Now showing items 1-5 of 5
The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves
We obtain new results concerning the Sato-Tate conjecture on the distribution of Frobenius traces over single and double parametric families of elliptic curves. We consider these curves for values of parameters having ...
On the number of rational points on special families of curves over function fields
We construct families of curves which provide counterexamples for a uniform boundedness question. These families generalize those studied previously by several authors. We show, in detail, what fails in the argument ...
Visible Points on Curves over Finite Fields
For a prime 𝑝 and an absolutely irreducible modulo 𝑝 polynomial 𝑓(U,V) ∈ ℤ[U,V] we obtain an asymptotic formulas for the number of solutions to the congruence 𝑓(𝑥,𝑦) ≡ a (mod 𝑝) in positive integers 𝑥 ⩽ X, 𝑦 ...
Torsion points on y²=x⁶+1
Let C be the curve y²=x⁶+1 of genus 2 over a field of characteristic zero. Consider C embedded in its Jacobian J by sending one of the points at infinity on C to the origin of J. In this brief note we show that the ...
The d-primary Brauer-Manin obstruction for Curves
For a curve over a global field we consider for which integers d the d-primary part of the Brauer group can obstruct the existence of rational points. We give examples showing it is possible that there is a d-primary ...