Abstract
We prove effective bounds for the set of quasi-integral points in orbits of rational maps over function fields under some conditions, generalizing previous work of Hsia and Silverman (Pacific J Math 249(2), 321–342, 2011) for orbits over function fields of characteristic zero. We then use this to prove height bounds for algebraic functions whose orbit under a rational function has multiplicative dependent elements modulo groups of S-units, generalizing recent results over number fields.
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The Project is funded by Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada.
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The author thanks the Australian Research Council Discovery Grant DP180100201, NSERC, and Oakland University for supporting him in this work.
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Mello, J. On effective \(\epsilon \)-integrality in orbits of rational maps over function fields and multiplicative dependence. European Journal of Mathematics 9, 112 (2023). https://doi.org/10.1007/s40879-023-00709-x
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DOI: https://doi.org/10.1007/s40879-023-00709-x