Abstract
We give a parameterization of the algebraic points of given degree over $\mathbb{Q}$ on the Picard curve given by $y^{3}=x^{4}-1$. This result extends a previous result of Klassen and Schaefer(1996) on the set of algebraic points of degree at most $3$ over $\mathbb{Q}$ in the same curve.
Information
Published: 1 January 2018
First available in Project Euclid: 26 September 2019
Digital Object Identifier: 10.16929/sbs/2018.100-01-04
Subjects:
Primary:
11D68
,
12F05
,
14H50
,
14hH40
Keywords:
algebraic points of given degree
,
Jacobian
,
linear system
,
Picard curve
Rights: Copyright © 2018 The Statistics and Probability African Society
