English

Counting points by height in semigroup orbits

Number Theory 2024-12-04 v1 Dynamical Systems

Abstract

We improve known estimates for the number of points of bounded height in semigroup orbits of polarized dynamical systems. In particular, we give exact asymptotics for generic semigroups acting on the projective line. The main new ingredient is the Wiener-Ikehara Tauberian theorem, which we use to count functions in semigroups of bounded degree.

Keywords

Cite

@article{arxiv.2305.04960,
  title  = {Counting points by height in semigroup orbits},
  author = {Jason P. Bell and Wade Hindes and Xiao Zhong},
  journal= {arXiv preprint arXiv:2305.04960},
  year   = {2024}
}
R2 v1 2026-06-28T10:29:04.744Z