On the typical rank of elliptic curves over Q(T)

Francesco Battistoni, Sandro Bettin, Christophe Delaunay*

*Autore corrispondente per questo lavoro

Risultato della ricerca: Contributo in rivistaArticolo in rivista

Abstract

As an application of Turán sieve, we give upper bounds for the number of elliptic curves defined over Q(T) in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan’s conjecture (Cowan in Conjecture: 100% of elliptic surfaces over Q have rank zero. Preprint. https://arxiv.org/pdf/2009.08622.pdf, 2020) in the case m, n≤ 2.
Lingua originaleEnglish
pagine (da-a)N/A-N/A
RivistaResearch in Number Theory
Volume8
DOI
Stato di pubblicazionePubblicato - 2022

Keywords

  • Elliptic curves
  • Rank
  • Rational points

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