English

Horocycle flow at product of two primes

Dynamical Systems 2024-09-26 v1 Number Theory

Abstract

We show that if Γ\Gamma is a co-compact arithmetic lattice in SL(2,R)SL(2,\mathbb{R}) or Γ=SL(2,Z)\Gamma=SL(2,\mathbb{Z}) then the horocycle orbit of every non-periodic point xSL(2,R)/Γx\in SL(2,\mathbb{R})/\Gamma equidistributes (with respect to Haar measure) when sampled at integers having exactly two prime factors.

Keywords

Cite

@article{arxiv.2409.16687,
  title  = {Horocycle flow at product of two primes},
  author = {Giovanni Forni and Adam Kanigowski and Maksym Radziwiłł},
  journal= {arXiv preprint arXiv:2409.16687},
  year   = {2024}
}