Nombres premiers de la forme \([n^c]\). (Prime numbers of the form \([n^c]\)) (Q2715676)
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scientific article; zbMATH DE number 1599833
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nombres premiers de la forme \([n^c]\). (Prime numbers of the form \([n^c]\)) |
scientific article; zbMATH DE number 1599833 |
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20 May 2001
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prime number theorem of Piatetski-Shapiro
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exponential sums
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Nombres premiers de la forme \([n^c]\). (Prime numbers of the form \([n^c]\)) (English)
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Let \(\pi_c(x)=\sum _{n\leq x,[n^c]\text{prime}}1\), then the authors prove, that the asymptotic equation \(\pi_c(x)= {x\over c\log c}(1+ o(1))\) \((x\to\infty)\) holds for \(1<c< {2817\over 2426}= 1,16117\dots\).NEWLINENEWLINENEWLINEThis is the so-called prime number theorem of Piatetski-Shapiro for an extended range of the exponent \(c\). The authors use refined estimates for exponential sums.
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