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arXiv · 2109.00745

On the typical rank of elliptic curves over ${\mathbb Q}(T)$

Francesco Battistoni·Sandro Bettin·Christophe Delaunay
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Abstract

We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan's conjecture (arXiv:2009.08622v2) in the case $m,n\leq2$.

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Francesco Battistoni, Sandro Bettin, Christophe Delaunay. 2022-03-29. On the typical rank of elliptic curves over ${\mathbb Q}(T)$. https://arxiv.org/abs/2109.00745

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