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math.NT2018
and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve
Beth Romano, Jack A. Thorne
We prove that the average size of the 3-Selmer group of a genus-2 curve with a marked Weierstrass point is 4.
math.NT2017
On the arithmetic of simple singularities of type E
Beth Romano, Jack A. Thorne
An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exc…