Chennai Mathematical Institute

Seminars




12.00 noon
The boundedness of the average rank of elliptic curves

Arul Shankar
Princeton University, U.S.A.
10-08-10


Abstract

The purpose of this talk is to prove that the average rank of elliptic curves when ordered by their heights is bounded. This is accomplished by bounding the mean size of the 2- and 3-Selmer groups of elliptic curves. As a consequence we deduce that a positive proportion of elliptic curves, when ordered by height, have rank 0. This is joint work with Professor Manjul Bhargava.





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