Properties of the function f ( x ) = x / π ( x )

Panayiotis Vlamos

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 28, 1-5

Abstract:

We obtain the asymptotic estimations for ∑ k = 2 n f ( k ) and ∑ k = 2 n 1 / f ( k ) , where f ( k ) = k / π ( k ) , k ≥ 2 . We study the expression 2 f ( x + y ) − f ( x ) − f ( y ) for integers x , y ≥ 2 and as an application we make several remarks in connection with the conjecture of Hardy and Littlewood.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:971945

DOI: 10.1155/S0161171201005725

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