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 | English |
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pagine (da-a) | N/A-N/A |
Rivista | Research in Number Theory |
Volume | 8 |
DOI | |
Stato di pubblicazione | Pubblicato - 2022 |
Keywords
- Elliptic curves
- Rank
- Rational points