Ilya Shkredov

On Korobov's bound concerning Zaremba's conjecture.

We prove in particular that for any sufficiently large prime p, there exists 1 <= a< p such that all partial quotients of a/p are bounded by O(\log p/\log \log p). This improves the well-known Korobov bound concerning Zaremba's conjecture from the theory of continued fractions. Joint work with N.G. Moshchevitin and B. Murphy.