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On the distribution of prime numbers of the form [nc]

Published online by Cambridge University Press:  19 July 2001

A. KUMCHEV
A. KUMCHEV
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC29208, USA; e-mail: koumtche@math.sc.edu
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Abstract

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Let πc(x) be the number of the integers n≤x such that [nc] is prime. We shall prove that $$π_{c}\tfrm{(}x\tfrm{)&2_Gt;}{x\over \log x}$$ for 1<c<45/38. This improves the former range 1<c<13/11.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 1 , March 1999 , pp. 85 - 102
Copyright
1999 Glasgow Mathematical Journal Trust