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Mathematics of Computation

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Computing points of bounded height in projective space over a number field

Author: David Krumm
Journal: Math. Comp. 85 (2016), 423-447
MSC (2010): Primary 11Y40
Published electronically: June 9, 2015
MathSciNet review: 3404456
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Abstract: We construct an algorithm for solving the following problem: given a number field $K$, a positive integer $N$, and a positive real number $B$, determine all points in $\mathbb {P}^N(K)$ having relative height at most $B$. A theoretical analysis of the efficiency of the algorithm is provided, as well as sample computations showing how the algorithm performs in practice. Two variants of the method are described, and examples are given to compare their running times. In the case $N=1$ we compare our method to an earlier algorithm for enumerating elements of bounded height in number fields.

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Additional Information

David Krumm
Affiliation: Department of Mathematics, Claremont McKenna College, Claremont, California 91711

Received by editor(s): April 10, 2014
Received by editor(s) in revised form: August 2, 2014
Published electronically: June 9, 2015
Article copyright: © Copyright 2015 American Mathematical Society