The Probability of Primality of the Order of a Genus 2 Curve Jacobian
110 views · Published 17 August 2016 · 57:40 · Indexed 20 September 2026
Channel: Microsoft Research · 2016 · Science & Technology
In 2000, Galbraith and McKee conjectured a formula estimating the probability of primality of the number of rational points on an elliptic curve over a finite field. Their heuristic derivation was based on an analytic class number formula counting bivariate quadratic forms up to equivalence. We will give alternative heuristics in favor of the conjecture, based on a random matrix model. This approach seems better-suited for generalizing the conjecture to curves of higher genus. We will then elaborate this in genus 2. This is joint work with Hendrik Hubrechts and Alessandra Rigato.
