Canonical heights on Pell conics over number fields
DOI:
https://doi.org/10.52737/18291163-2020.12.5-1-9Keywords:
canonical height, Pell conicAbstract
In "Higher descent on Pell conics. III. The first 2-descent", Lemmermeyer introduced the canonical heights on the groups of rational points on Pell conics, which are analogues of the canonical heights on elliptic curves. In this paper, we generalize this: We introduce the canonical heights on the groups of $\overline{\mathbb{Q}}$-rational points on Pell conics over number fields.
References
E. Bombieri and W. Gubler, Heights in Diophantine Geometry, New Mathematical Monographs, 4. Cambridge University Press, Cambridge, 2006.
F. Lemmermeyer, Higher descent on Pell conics. III. The first 2-descent, preprint, available at: https://arxiv.org/abs/math/0311310
P. Shastri, Integral points on the unit circle, J. Number Theory, 91 (2001), no. 1, pp. 67-70. https://doi.org/10.1006/jnth.2000.2635
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