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On the sign changes of (π(x)-lix). II

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Abstract

If π(x) stands for the number of primes not exceedingx then the existence of two effectively calculable constantsc 1 andc 2 is proved so that forT>c 1, the numberV(T) of sign changes of\(\left( {\pi (x) - \int\limits_2^x {dv} /logv} \right)\) in (0,T) is greater thanc 2logloglogT.

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Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda Utca 13-15, 1053, Budapest V, Hungary

    S. Knapowski & P. Turán

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  1. S. Knapowski
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  2. P. Turán
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Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday

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Knapowski, S., Turán, P. On the sign changes of (π(x)-lix). II. Monatshefte für Mathematik 82, 163–175 (1976). https://doi.org/10.1007/BF01305997

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