A local limit theorem with speed of convergence for Euclidean algorithms and diophantine costs

Viviane Baladi, Aïcha Hachemi

For large $N$, we consider the ordinary continued fraction of $x=p/q$ with $1\le p\le q\le N$, or, equivalently, Euclid's gcd algorithm for two integers $1\le p\le q\le N$, putting…