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

Francesco Battistoni; Sandro Bettin; Christophe Delaunay

doi:10.1007/s40993-022-00377-y

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

Francesco Battistoni, Sandro Bettin, Christophe Delaunay^*

^*Corresponding author

Research output: Contribution to journal › Article

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.

Original language	English
Pages (from-to)	N/A-N/A
Journal	Research in Number Theory
Volume	8
DOIs	https://doi.org/10.1007/s40993-022-00377-y
Publication status	Published - 2022

Keywords

Elliptic curves
Rank
Rational points

Access to Document

10.1007/s40993-022-00377-y

Cite this

@article{52fb32f9b9d24362ae1ef9a5e9550d79,

title = "On the typical rank of elliptic curves over Q(T)",

abstract = "As an application of Tur{\'a}n 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{\textquoteright}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.",

keywords = "Elliptic curves, Rank, Rational points, Elliptic curves, Rank, Rational points",

author = "Francesco Battistoni and Sandro Bettin and Christophe Delaunay",

year = "2022",

doi = "10.1007/s40993-022-00377-y",

language = "English",

volume = "8",

pages = "N/A--N/A",

journal = "Research in Number Theory",

issn = "2363-9555",

publisher = "SpringerOpen",

}

TY - JOUR

T1 - On the typical rank of elliptic curves over Q(T)

AU - Battistoni, Francesco

AU - Bettin, Sandro

AU - Delaunay, Christophe

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Elliptic curves

KW - Rank

KW - Rational points

KW - Elliptic curves

KW - Rank

KW - Rational points

UR - http://hdl.handle.net/10807/270244

U2 - 10.1007/s40993-022-00377-y

DO - 10.1007/s40993-022-00377-y

M3 - Article

SN - 2363-9555

VL - 8

SP - N/A-N/A

JO - Research in Number Theory

JF - Research in Number Theory

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this