The distribution of \(\alpha p\) modulo one (Q2766442)
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scientific article; zbMATH DE number 1696355
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The distribution of \(\alpha p\) modulo one |
scientific article; zbMATH DE number 1696355 |
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28 January 2002
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The distribution of \(\alpha p\) modulo one (English)
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Let \(\|x\|\) be the distance from \(x\) to the nearest integer, and let \(\alpha\) be an irrational number. Then the authors prove that for any \(\varepsilon> 0\) there are infinitely many prime numbers \(p\) such that \(\|\alpha p\|< p^{-16/49+ \varepsilon}\), improving the value \(9/28\) of \textit{C. Jia} [Sci. China, Ser. A 43, 703-721 (2000; Zbl 0982.11039)]. They use sieve methods combined with estimates of tri-linear sums.
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