The intersection of Piatetski-Shapiro sequences (Q2874613)
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scientific article; zbMATH DE number 6327858
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The intersection of Piatetski-Shapiro sequences |
scientific article; zbMATH DE number 6327858 |
Statements
8 August 2014
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Piatetski-Shapiro sequences
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sums over primes
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exponential sums
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asymptotics
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The intersection of Piatetski-Shapiro sequences (English)
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The author has proved an asymptotic formula for the number of primes \(p\), \(p\leq x\), where NEWLINE\[NEWLINEp=[n^{c_1}_1]= [n^{c_2}_n]=\cdots= [n^{c_d}_d],NEWLINE\]NEWLINE with \(c_1,c_2,\dots, c_d\) being sufficiently close to 1, but greater than 1. Here \([x]\) stands for the integer part of the real number \(x\).NEWLINENEWLINE An improvement of an earlier result of \textit{E. R. Sirota} [Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 121, 94--102 (1983; Zbl 0524.10038)], for the case \(d=2\) and \textit{W. Zhai} [Sci. China, Ser. A 42, No. 11, 1173--1183 (1999; Zbl 0964.11040)], for the case \(d\geq 3\) is presented.
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