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

Francesco Battistoni; S. Bettin; C. Delaunay

doi:10.1007/s40993-022-00377-y

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

Francesco Battistoni
, S. Bettin
, C. Delaunay^*

^*Autore corrispondente per questo lavoro

University of Genoa
CNRS

Risultato della ricerca: Contributo in rivista › Articolo

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 originale	Inglese
pagine (da-a)	N/A-N/A
Rivista	Research in Number Theory
Volume	8
Numero di pubblicazione	4
DOI	https://doi.org/10.1007/s40993-022-00377-y
Stato di pubblicazione	Pubblicato - 2022

All Science Journal Classification (ASJC) codes

Algebra e Teoria dei Numeri

Keywords

Elliptic curves
Rank
Rational points

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10.1007/s40993-022-00377-y

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KW - Rational points

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KW - Rank

KW - Rational points

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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