Diophantine approximation with smooth numbers
نویسندگان
چکیده
Let \(\theta \) be an irrational number and \(\varphi a real number. \(C > 2\) \(\varepsilon 0\). There are infinitely many positive integers n free of prime factors \(> (\log )^C\), such that \(\Vert \theta + \varphi \Vert < n^{-\left( \frac{1}{3} - \frac{2}{3C}\right) \varepsilon }\). Here y\Vert is the distance from y to \(\mathbb Z\).
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ژورنال
عنوان ژورنال: Ramanujan Journal
سال: 2021
ISSN: ['1572-9303', '1382-4090']
DOI: https://doi.org/10.1007/s11139-020-00361-z