On certain inequalities for the prime counting function

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 149—153
DOI: 10.7546/nntdm.2021.27.4.149-153
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Authors and affiliations

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

Abstract

We study certain inequalities for the prime counting function π(x). Particularly, a new proof and a refinement of an inequality from [1] is provided.

Keywords

  • Prime counting function
  • Inequalities
  • Hardy–Littlewood conjecture

2020 Mathematics Subject Classification

  • 11A25
  • 11A41

References

  1. Alzer, H., Kwong, M. K., & Sándor, J. (2021). Inequalities for π(x). Rendiconti del Seminario Matematico della Universita di Padova, 145(2), 1–15 (to appear).
  2. Panaitopol, L. (2001). Some generalizations for a theorem by Landau. Mathematical Inequalities & Applications, 4(3), 327–330.
  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., & Crstici, B. (2006). Handbook of Number Theory. I, Springer.
  5. Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions, Nova Science Publishers, New York.
  6. Segal, S. L. (1962). On π(x+y) π(x)+π(y). Transactions of the American Mathematical Society, 104, 523–527.

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Cite this paper

Sándor, J. (2021). On certain inequalities for the prime counting function. Notes on Number Theory and Discrete Mathematics, 27(4), 149-153, doi: 10.7546/nntdm.2021.27.4.149-153.

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