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Primes of the form [pc] and related questions

Published online by Cambridge University Press:  18 May 2009

Glyn Harman  and
Joël Rivat
Glyn Harman
Affiliation:
School of Mathematics, UWCC, Senghennydd Road, P.O. Box 926, Cardiff CF2 4YH
Joël Rivat
Affiliation:
Bâtiment 425, Université de Paris Sud, 91405 Orsay, France, rivat@matups.matups.fr
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Much interest has been shown in determining the range of values of c for which the sequence [n]c contains infinitely many primes. The result is an elementary deduction from the prime number theorem, of course, of 0<c≤l. In 1953, Piatetski–Shapiro [9] showed that

for 1<c<12/11, where xc(X) stands for the number of primes in the set {[nc]n≤x}.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 2 , May 1995 , pp. 131 - 141
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

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