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Counting points of bounded relative height

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  26 February 2010

Ana-Cecilia de la Maza
Ana-Cecilia de la Maza
Affiliation:
Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
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Abstract

Let L/K be an extension of number fields and let be the subgroup of the unit group consisting of the elements that are roots of units of . Denote by (L/K, B) the number of points in with relative height in the sense of Bergé-Martinet at most B. Here ℙ1(L) stands for the one-dimensional projective space over L. In this paper is proved the formula (L/K, B) = CB2 + O(B2−1/[L:Q]), where C is a constant given in terms of invariants of L/K such as the regulators, class number and discriminant.

MSC classification

Secondary: 11R04: Algebraic numbers; rings of algebraic integers
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 125 - 152
Copyright
Copyright © University College London 2003

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