Equidistribution of continued fraction convergents in $\mathrm{SL}(2,{\mathbb{Z}}_m)$ with an application to local discrepancy

Bence Borda

Consider the sequence of continued fraction convergents $p_n/q_n$ to a random irrational number. We study the distribution of the sequences $p_n(\mathrm{mod}m)$ and $q_n(\mathrm{mod}m)$ with a…