TY - JOUR
T1 - On the typical rank of elliptic curves over Q(T)
AU - Battistoni, Francesco
AU - Bettin, S.
AU - Delaunay, C.
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 - https://publicatt.unicatt.it/handle/10807/270244
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85138100752&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85138100752&origin=inward
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
IS - 4
ER -