On the sign changes in the remainder term of an asymptotic formula for the number of square-free numbers (Q1325097)
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scientific article; zbMATH DE number 571897
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sign changes in the remainder term of an asymptotic formula for the number of square-free numbers |
scientific article; zbMATH DE number 571897 |
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On the sign changes in the remainder term of an asymptotic formula for the number of square-free numbers (English)
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24 May 1994
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Let \(\Delta(x)= \sum_{n\leq x} |\mu (n)|- {x\over {\zeta(2)}}\) where \(\mu\) denotes the Möbius function, and let \(V(T)\) denote the number of changes of sign of \(\Delta(x)\) in \([2,T]\). The author proves that for all sufficiently large \(T\) the inequality \(V(T)\geq AT\) holds with an effective constant \(A>0\).
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sign changes
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remainder term
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asymptotic formula
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square-free numbers
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Möbius function
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0.81333988904953
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0.8070963025093079
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0.8008043766021729
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0.782122790813446
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