English

Points of bounded height on oscillatory sets

Algebraic Geometry 2017-04-18 v3 Number Theory

Abstract

We show that transcendental curves in Rn\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 x2y+xy+cy=0x^2y''+xy'+cy=0 with c>0c>0.

Keywords

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}
}
R2 v1 2026-06-22T12:28:10.165Z