1College of Industrial Technology Nihon University 2-11-1 Shin-ei Narashino, Chiba 275-8576, Japan 2Faculty of Engineering Tohoku-Gakuin University 1-13-1 Chuo Tagajo, Miyagi 985-8537, Japan
We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell–Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.
Keywords:
study integral points generators cubic twists fermat cubic curve main results assert integral points system generators where mordell weil rank corollary explicitly describe integral points curve
Affiliations des auteurs :
Yasutsugu Fujita
1
;
Tadahisa Nara
2
1
College of Industrial Technology Nihon University 2-11-1 Shin-ei Narashino, Chiba 275-8576, Japan
2
Faculty of Engineering Tohoku-Gakuin University 1-13-1 Chuo Tagajo, Miyagi 985-8537, Japan
@article{10_4064_aa168_1_1,
author = {Yasutsugu Fujita and Tadahisa Nara},
title = {Generators and integral points on twists of the {Fermat} cubic},
journal = {Acta Arithmetica},
pages = {1--16},
year = {2015},
volume = {168},
number = {1},
doi = {10.4064/aa168-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa168-1-1/}
}
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AU - Tadahisa Nara
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%J Acta Arithmetica
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%N 1
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Yasutsugu Fujita; Tadahisa Nara. Generators and integral points on twists of the Fermat cubic. Acta Arithmetica, Tome 168 (2015) no. 1, pp. 1-16. doi: 10.4064/aa168-1-1
