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Article Dans Une Revue Research in Number Theory Année : 2022

On the typical rank of rational elliptic surfaces

Résumé

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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hal-03334057 , version 1 (03-09-2021)

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Francesco Battistoni, Sandro Bettin, Christophe Delaunay. On the typical rank of rational elliptic surfaces. Research in Number Theory, 2022. ⟨hal-03334057⟩
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