论文标题
关于Zaremba的猜想，在Korobov上
On Korobov bound concerning Zaremba's conjecture
论文作者
论文摘要
我们特别证明，对于任何足够大的prime $ p $，有$ 1 \ le a <p $，以便所有$ a/p $的偏部分都由$ o（\ log p/\ log log \ log \ log p）$界定。对于复合分母，获得了类似的结果。这改善了井的众所周知的关于Zaremba从持续分数理论中的猜想的约束。
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.
