#### Vol. 15, No. 3, 2021

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The geometric average size of Selmer groups over function fields

### Aaron Landesman

Vol. 15 (2021), No. 3, 673–709
##### Abstract

We show, in the large $q$ limit, that the average size of $n$-Selmer groups of elliptic curves of bounded height over ${\mathbb{𝔽}}_{q}\left(t\right)$ 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 ${\mathbb{𝔽}}_{q}\left(t\right)$ have rank $0$ or $1$.

##### Keywords
Selmer groups, arithmetic statistics, function fields, moduli stacks
Primary: 11G05