Natural Sciences, Mathematics, 2026
Canonical heights on Pell conics over number fields
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Submitted: 2024-12-09
© 2026 by author(s) and The Gufo Inc.
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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.