### On Korobov's bound concerning Zaremba's conjecture.

Combinatorics Seminar

2nd March 2023, 11:00 am – 12:00 pm

Fry Building, G.07

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.

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