Event Type
Seminar
Monday, May 6, 2019 2:30 PM
Wei Ho (MSRI/University of Michigan)

We show that the second moment for the number of integral points on elliptic curves over
Q is bounded. The main new ingredient in our proof is an upper bound on the number of
integral points on an affine integral Weierstrass model of an elliptic curve depending only on
the rank of the curve and the square divisors of the discriminant.

We obtain the bound by studying a bijection first observed by Mordell between integral points on these curves and certain types of binary quartic forms. The results on moments then follow from Holders inequality, analytic techniques, and results on bounds on the average sizes of Selmer groups in the families. This is joint work with Levent Alpoge.