Additive functions with bounded difference (Q1231928)
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scientific article; zbMATH DE number 3533001
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Additive functions with bounded difference |
scientific article; zbMATH DE number 3533001 |
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Additive functions with bounded difference (English)
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1979
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A short and elementary proof is given that if \(f\) is an additive arithmetic function and \(f(n+1) - f(n)\) is bounded from one side, then it must be bounded from both sides. According to a famous theorem of Wirsing, this implies that these functions have the form \(f(n)=c\log n+O(1)\).
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