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On Pjateckiǐ-Šapiro prime number theorem. (English) Zbl 0795.11038
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.

##### MSC:
 11N05 Distribution of primes 11N36 Applications of sieve methods 11L07 Estimates on exponential sums