Schnirelmann density of the sequence \([\alpha n]\) (Q1911820)
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scientific article; zbMATH DE number 870996
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Schnirelmann density of the sequence \([\alpha n]\) |
scientific article; zbMATH DE number 870996 |
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Schnirelmann density of the sequence \([\alpha n]\) (English)
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25 March 1997
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For an irrational number \(\alpha\) let \(A\) be the set of integers of the form \([\alpha n]\). The Schnirelmann density of these sets is calculated. Since this is 0 for \(\alpha>2\), for this case the author also calculates \(\sigma (A\cup\{1\})\) and his `modified Schnirelmann density' defined by \[ \sigma'(A) = \inf_{A(n) \geq 1} A(n)/n. \]
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Schnirelmann density
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