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 . 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