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A lower bound on the canonical height for polynomials

  • Nicole Looper
Article
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Abstract

We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and the number of places of bad reduction.

Mathematics Subject Classification

11G50 37P30 37P45 37P15 

Notes

Acknowledgements

I would like to thank Laura DeMarco for introducing me to the trees in [6] and [7], and for many helpful and enlightening discussions on that topic. I would also like to thank Patrick Ingram for several fruitful conversations on this research problem, and for sharing his results concerning the normal form used throughout this article. Finally, it is a pleasure to thank Laura DeMarco and Joseph Silverman for their useful comments on an earlier draft, and the anonymous referee for his or her careful reading and additional suggestions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

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