Most odd degree hyperelliptic curves have only one rational point

Most odd degree hyperelliptic curves have only one rational point - Bjorn Poonen

Bjorn Poonen
Massachusetts Institute of Technology
March 26, 2015
We prove that the probability that a curve of the form $y^2 = f(x)$ over $\mathbb Q$ with $\deg f = 2g + 1$ has no rational point other than the point at infinity tends to 1 as $g$ tends to infinity. This is joint work with Michael Stoll.