English

Expansion in $\text{SL}_2(\mathbb Z/q\mathbb Z)$ and Zaremba's conjecture

Number Theory 2026-05-11 v2

Abstract

We establish an expansion theory for SL2(Z/qZ)\text{SL}_2(\mathbb Z/q\mathbb Z). Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.

Keywords

Cite

@article{arxiv.2605.02518,
  title  = {Expansion in $\text{SL}_2(\mathbb Z/q\mathbb Z)$ and Zaremba's conjecture},
  author = {Xin Zhang},
  journal= {arXiv preprint arXiv:2605.02518},
  year   = {2026}
}

Comments

Typos in v1 corrected