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arXiv · 2212.14646

On Korobov bound concerning Zaremba's conjecture

Nikolay Moshchevitin·Brendan Murphy·Ilya Shkredov
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Abstract

We prove in particular that for any sufficiently large prime $p$ there is $1\le a<p$ such that all partial quotients of $a/p$ are bounded by $O(\log p/\log \log p)$. 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.

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Nikolay Moshchevitin, Brendan Murphy, Ilya Shkredov. 2022-12-30. On Korobov bound concerning Zaremba's conjecture. https://arxiv.org/abs/2212.14646

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