On the Pjateckii-Šapiro prime number theorem. (English) Zbl 0772.11032

Liu, H. Q.; Rivat, J.

Bull. Lond. Math. Soc. 24, No. 2, 143-147 (1992).

I. I. Piatetski-Shapiro [Mat. Sb., Nov. Ser. 33, 559-566 (1953; Zbl 0053.027)] proved the extraordinary result that, for any positive \(c<12/11\), the number of integers \(n\leq x\) for which the integer part of \(n^ c\) is prime, is asymptotically \(x/c\log x\). There have been various papers which show this result for larger and larger values of \(c\), and herein the authors show it for any \(c<15/13\), a new record.

Reviewer: A.Granville (Athens / Georgia)

MSC:

11N05

Distribution of primes

Keywords:

Piatetski-Shapiro problem

Citations:

Zbl 0053.027