Points of bounded height on oscillatory sets - Université Grenoble Alpes
Article Dans Une Revue Quart. J. Math. Oxford Année : 2017

Points of bounded height on oscillatory sets

Résumé

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 $c>0$.

Dates et versions

hal-04709681 , version 1 (25-09-2024)

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Citer

Georges Comte, Chris Miller. Points of bounded height on oscillatory sets. Quart. J. Math. Oxford, 2017, ⟨doi:10.1093/qmath/hax021⟩. ⟨hal-04709681⟩

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