Arul Shankar, University of Toronto
Ranks of elliptic curves are often studied via their 2-Selmer groups. It is known that the average size of the 2-Selmer group of elliptic curves is 3, when the family of all elliptic curves is ordered by (naive) height. On the computational side, Balakrishnan, Ho, Kaplan, Spicer, Stein, and Weigand collect and analyze data on ranks, 2-Selmer groups, and other arithmetic invariants of elliptic curves, when ordered by height. Interestingly, they find a persistently smaller average size of the 2-Selmer group in the data. Thus it is natural to ask whether there exists a second order main term in the counting function of the 2-Selmer groups of elliptic curves. In this talk, I will discuss joint work with Takashi Taniguchi, in which we prove the existence of such a secondary term.
MC 5501