On Pjateckiǐ-Šapiro prime number theorem (Q1327000)
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scientific article; zbMATH DE number 589863
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Pjateckiǐ-Šapiro prime number theorem |
scientific article; zbMATH DE number 589863 |
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On Pjateckiǐ-Šapiro prime number theorem (English)
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7 July 1994
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The author proves that, if \(1<c<20/17\), then the number of primes having the form \([n^ c]\) with \(n\leq x\) is \(\gg x/\log x\). He has subsequently improved this to \(1<c<13/11\) in his second paper [Sci. China, Ser. A 36, No. 8, 913-926 (1993; Zbl 0790.11063)], which has already been reviewed.
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prime number theorem
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sieve methods
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Piatetski-Shapiro theorem
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estimates for trigonometric sums
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