Canonical heights on Pell conics over number fields

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 Q-rational points on Pell conics over number fields.