Most odd degree hyperelliptic curves have only one rational point

Most odd degree hyperelliptic curves have only one rational point

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Bjorn Poonen, MIT
TBD

We prove that the probability that a curve of the form y^2 = f(x) over 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.