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Now showing items 1-5 of 5

#### The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves

(2015)

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

(2016)

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

(2013)

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

(1997)

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

(2017)

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
...