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arXiv · 1601.03033

Points of bounded height on oscillatory sets

Georges Comte·Chris Miller
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Abstract

We show that transcendental curves in $\mathbb R^n$ (not necessarily compact) have few rational points of bounded height provided that the curves are well behaved with respect to algebraic sets in a certain sense and can be parametrized by functions belonging to a specified algebra of infinitely differentiable functions. Examples of such curves include logarithmic spirals and solutions to Euler equations $x^2y''+xy'+cy=0$ with $c>0$.

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Georges Comte, Chris Miller. 2016-01-12. Points of bounded height on oscillatory sets. https://arxiv.org/abs/1601.03033

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