3 papers
math.AG2020
Kummer surfaces for primality testing
Eduardo Ruíz Duarte, Marc Paul Noordman
We use the arithmetic of the Kummer surface associated to the Jacobian of a hyperelliptic curve to study the primality of integers of the form . We provide an algorithm…
math.AG2019
A proof of the Hasse-Weil inequality for genus 2 à la Manin
Eduardo Ruíz Duarte, Jaap Top
We prove the Hasse-Weil inequality for genus 2 curves given by an equation of the form y^2 = f(x) with f a polynomial of degree 5, using arguments that mimic the elementary proof o…
math.NT2017
Geometric primality tests using curves of genus 1 & 2
Eduardo Ruiz Duarte
We revisit and generalize some geometric techniques behind deterministic primality testing for some integer sequences using curves of genus 1 over finite rings. Subsequently we dev…