On the distribution of \(\{{x\over n}\}\) (Q1312937)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the distribution of \(\{{x\over n}\}\) |
scientific article; zbMATH DE number 495870
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the distribution of \(\{{x\over n}\}\) |
scientific article; zbMATH DE number 495870 |
Statements
On the distribution of \(\{{x\over n}\}\) (English)
0 references
31 July 1994
0 references
Let \(L_ R(x;\alpha)\) be the number of positive integers \(n\) such that \(\{{x\over n}\}\leq\alpha< \{{x\over n}\}+ {R\over n}\), where \(\alpha\in [0,1)\) and \(\{x\}\) means the fractional part of \(x\). The main result is that \(L_ R(x,\alpha)\ll Rx^ \varepsilon\) for \(R>x^{(\kappa+\lambda)/ (1+2\lambda)}\), where \((\kappa,\lambda)\) is an exponent pair.
0 references
divisor problem
0 references
fractional parts
0 references
exponent pair
0 references
