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arXiv · 2004.10594

Heights of Function Field Points on Curves Given by Equations with Separated Variables

Ta Thi Hoai An·Nguyen Ngoc Diep
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Abstract

Let $P$ and $Q$ be polynomials in one variable over an algebraically closed field $k$ of characteristic zero. Let $f$ and $g$ be elements of a function field $\K$ over $k$ such that $P(f)=Q(g).$ We give conditions on $P$ and $Q$ such that the height of $f$ and $g$ can be effectively bounded, and moreover, we give sufficient conditions on $P$ and $Q$ under which $f$ and $g$ must be constant.

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Ta Thi Hoai An, Nguyen Ngoc Diep. 2020-04-22. Heights of Function Field Points on Curves Given by Equations with Separated Variables. https://arxiv.org/abs/2004.10594

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