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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing points of bounded height in projective space over a number field
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by David Krumm PDF
Math. Comp. 85 (2016), 423-447 Request permission

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
  • Email: dkrumm@cmc.edu
  • Received by editor(s): April 10, 2014
  • Received by editor(s) in revised form: August 2, 2014
  • Published electronically: June 9, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 423-447
  • MSC (2010): Primary 11Y40
  • DOI: https://doi.org/10.1090/mcom/2984
  • MathSciNet review: 3404456