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On Korobov bound concerning Zaremba's conjecture
Published 30 Dec 2022 in math.NT and math.CO | (2212.14646v1)
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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