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Bemerkungen zur Arbeit von S. Knapowski und P. Turán

Notes to the paper of S. Knapowski and P. Turán

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Abstract

The present paper shows that by an easy modification of the ideas of S. Knapowski and P. Turán [2] one can prove the following

Theorem 1: LetV 1 (Y) denote the number of sign changes of π(x)−lix in the interval [2,Y. Then forY>C 1 the inequality

$$V_1 (Y) > C_2 (\log \log Y)C_3 $$

holds with positive effectively calculable constantsC 1, C2 andC 3.

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Literatur

  1. Ingham, A. E.: A note on the distribution of primes. Acta Arith.1, 201–211 (1936).

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  2. Knapowski, S., andP. Turán: On the sign changes of π(x)−li x , II. Mh. Math.82, 163–175 (1976).

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  3. Littlewood, J. E.: sur la distribution des nombres premiers. Comptes Rendus Paris158, 1869–1872 (1914).

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  4. Skewes, S.: On the difference π(x)−lix Proc. Lond. Math. Soc.5, 48–70 (1955).

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Authors and Affiliations

  1. Lehrstuhl für Algebra und Zahlentheorie, Eötvös Lorand Universität, Muzeum krt. 6-8, H-1088, Budapest, Ungarn

    J. Pintz

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  1. J. Pintz
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Additional information

Herrn Prof. Dr. E. Hlawka zum 60. Geburtstag gewidmet

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Pintz, J. Bemerkungen zur Arbeit von S. Knapowski und P. Turán. Monatshefte für Mathematik 82, 199–206 (1976). https://doi.org/10.1007/BF01526326

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  • DOI: https://doi.org/10.1007/BF01526326

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