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

Bounding Zaremba’s conjecture

Number theory

Using methods related to the Bourgain–Gamburd machine refines the previous bound on Zaremba’s conjecture in the theory of continued fractions.

On Korobov bound concerning Zaremba's conjecture

Submitted (2022)

N. Moshchevitin, B. Murphy, I. Shkredov

We prove in particular that for any sufficiently large prime pp there is 1ap1\leq a \leq p such that all partial quotients of a/pa/p are bounded by O(logp/loglogp)O(\log p/\log \log p). For composite denominators a similar result is obtained. This improves the well--known Korobov bound concerning Zaremba's conjecture from the theory of continued fractions.

Submitted (2022)

N. Moshchevitin, B. Murphy, I. Shkredov