A note on the distribution of values of an arithmetical function (Q1911894)
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scientific article; zbMATH DE number 871075
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the distribution of values of an arithmetical function |
scientific article; zbMATH DE number 871075 |
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A note on the distribution of values of an arithmetical function (English)
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11 September 1996
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Let \(k\) be a square-free number and \(\delta_k(n):= \max\{d\mid n: (d, k)= 1\}\). The authors study the function \[ V(\lambda):= \lim_{N\to \infty} {1\over N} \sum_{n\leq N,\;\delta_k(n)< n\lambda},\quad 0\leq \lambda\leq 1. \] They give a formula for \(V(\lambda)\) and an asymptotic expansion by applying the mean-value theorem of Delange.
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distribution of values
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arithmetic functions
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asymptotic expansion
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mean-value theorem of Delange
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0.8614488244056702
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0.7992879152297974
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