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Mathematics of Computation

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Computing canonical heights on the projective line with no factorization


Author: Elliot Wells
Journal: Math. Comp.
MSC (2010): Primary 37P30; Secondary 11G50, 11Y16
DOI: https://doi.org/10.1090/mcom/3200
Published electronically: April 7, 2017
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Abstract: We give an algorithm which requires no integer factorization for computing the canonical height of a point in $ \mathbb{P}^{1}(\mathbb{Q})$ relative to a morphism $ \phi : \mathbb{P}_{\mathbb{Q}}^{1} \rightarrow \mathbb{P}_{\mathbb{Q}}^{1}$ of degree $ d \geq 2$.


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Additional Information

Elliot Wells
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email: ellwells@math.brown.edu

DOI: https://doi.org/10.1090/mcom/3200
Received by editor(s): March 3, 2016
Received by editor(s) in revised form: July 12, 2016
Published electronically: April 7, 2017
Article copyright: © Copyright 2017 American Mathematical Society