Points of bounded height on oscillatory sets
Algebraic Geometry
2017-04-18 v3 Number Theory
Abstract
We show that transcendental curves in (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 with .
Cite
@article{arxiv.1601.03033,
title = {Points of bounded height on oscillatory sets},
author = {Georges Comte and Chris Miller},
journal= {arXiv preprint arXiv:1601.03033},
year = {2017}
}