On certain inequalities for the prime counting function – Part II

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 124—128
DOI: 10.7546/nntdm.2022.28.1.124-128
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Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University
Cluj-Napoca, Romania

Abstract

As a continuation of [6], we deduce some inequalities of a new type for the prime counting function π(x).

Keywords

  • Prime counting function
  • Inequalities
  • Hardy–Littlewood conjecture

2020 Mathematics Subject Classification

  • 11A25
  • 11A41

References

  1. Alzer, H., Kwong, M. K., & Sándor, J. Inequalities involving π(x). Rendiconti del Seminario Matematica della Universitá di Padova, pp. 1-15, to appear (Preprint published at the journal website).
  2. Panaitopol, L. (1999). Several approximations of π(x): Mathematical Inequalities and Applications, 2(3), 317–324.
  3. Rosser, J. B., & Schoenfeld, L. (1962). Approximate formulas for some functions of prime numbers. Illinois Journal of Mathematics, 6(1), 64–94.
  4. Sándor, J., Mitrinovic, D. S., & Cristici, B. (2006). Handbook of Number Theory, Vol. I, Springer.
  5. Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions. Nova Science Publ., New York.
  6. Sándor, J. (2021). On certain inequalities for the prime counting function. Notes on Number Theory and Discrete Mathematics, 27(4), 149–153.

Manuscript history

  • Received: 30 October 2021
  • Accepted: 11 February 2022
  • Online First: 28 February 2022

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Cite this paper

Sándor, J. (2022). On certain inequalities for the prime counting function – Part II. Notes on Number Theory and Discrete Mathematics, 28(1), 124-128, DOI: 10.7546/nntdm.2022.28.1.124-128.

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