Sums containing the fractional parts of numbers (Q1073079)
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scientific article; zbMATH DE number 3943940
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sums containing the fractional parts of numbers |
scientific article; zbMATH DE number 3943940 |
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Sums containing the fractional parts of numbers (English)
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1985
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An asymptotic formula for \(S=\sum_{n\leq x}n^ a \{x/n\}^ k\) is obtained where \(\{\) \(t\}\) is the fractional part of t. It is shown that \[ S=C x^{a+1}+O(x^{a+6/13}\quad \log^{7/13} x), \] where \(C=\int^{\infty}_{1}\{t\}^ k t^{-a-1} dt\).
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arithmetic sums
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asymptotic formula
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fractional part
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