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The geometric average size of Selmer groups over function fields
Algebra & Number Theory  (IF0.938),  Pub Date : 2021-05-20, DOI: 10.2140/ant.2021.15.673
Aaron Landesman

We show, in the large q limit, that the average size of n-Selmer groups of elliptic curves of bounded height over 𝔽q(t) is the sum of the divisors of n. As a corollary, again in the large q limit, we deduce that 100% of elliptic curves of bounded height over 𝔽q(t) have rank 0 or 1.