Integral points on cubic twists of Mordell curves
Chan S. 2023. Integral points on cubic twists of Mordell curves. Mathematische Annalen. 388(3), 2275β2288.
Download (ext.)
Journal Article
| Published
| English
Scopus indexed
Author
Abstract
Fix a non-square integer πβ 0. We show that the number of curves πΈπ΅:π¦^2=π₯^3+ππ΅^2 containing an integral point, where B ranges over positive integers less than N, is bounded by βͺππ(logπ)β1/2+π. In particular, this implies that the number of positive integers π΅β€π such that β3ππ΅^2 is the discriminant of an elliptic curve over π is o(N). The proof involves a discriminant-lowering procedure on integral binary cubic forms.
Publishing Year
Date Published
2023-02-07
Journal Title
Mathematische Annalen
Publisher
Springer Nature
Volume
388
Issue
3
Page
2275-2288
ISSN
eISSN
IST-REx-ID
Cite this
Chan S. Integral points on cubic twists of Mordell curves. Mathematische Annalen. 2023;388(3):2275-2288. doi:10.1007/s00208-023-02578-x
Chan, S. (2023). Integral points on cubic twists of Mordell curves. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-023-02578-x
Chan, Stephanie. βIntegral Points on Cubic Twists of Mordell Curves.β Mathematische Annalen. Springer Nature, 2023. https://doi.org/10.1007/s00208-023-02578-x.
S. Chan, βIntegral points on cubic twists of Mordell curves,β Mathematische Annalen, vol. 388, no. 3. Springer Nature, pp. 2275β2288, 2023.
Chan S. 2023. Integral points on cubic twists of Mordell curves. Mathematische Annalen. 388(3), 2275β2288.
Chan, Stephanie. βIntegral Points on Cubic Twists of Mordell Curves.β Mathematische Annalen, vol. 388, no. 3, Springer Nature, 2023, pp. 2275β88, doi:10.1007/s00208-023-02578-x.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Link(s) to Main File(s)
Access Level
Open Access
Export
Marked PublicationsOpen Data ISTA Research Explorer
Sources
arXiv 2203.11366
Google Scholar