Lifting all elements in ${\mathrm{SL}}_n(\mathbb{Z}/q\mathbb{Z})$

Amitay Kamber, Péter P. Varjú

We show that every element of ${\mathrm{SL}}_n(\mathbb{Z}/q\mathbb{Z})$ can be lifted to an element of ${\mathrm{SL}}_n(\mathbb{Z})$ of norm at most $C{q}^2\log q$, while there exist…