Armenian Journal of Mathematics, 12(5)
2022; 1–9
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Canonical heights on Pell conics over number fields

Masao Okazaki*

Received: 2024-12-10 · Published: 2022-08-30

© 2022 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Canonical heights on Pell conics over number fields
Author
Masao Okazaki
Source journal
Armenian Journal of Mathematics, 12(5)
Published
2022-08-30
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2020.12.5-1-9

Abstract

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 ¯¯¯¯QQ¯-rational points on Pell conics over number fields.
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