×

On some inequalities concerning \(\pi(x)\). (English) Zbl 1116.11317

Summary: We investigate the inequalities \(\pi(M+N)\leq a\pi(M/a)+\pi(N)\) and \(\pi(M+N)\leq a(\pi(M/a)+\pi(N/a))\) with \(a\geq 1\).

MSC:

11N05 Distribution of primes
PDF BibTeX XML Cite
Full Text: DOI Euclid EuDML

References:

[1] Clark D. A., Mathematics of Computation 70 (236) pp 1713– (2001) · Zbl 1030.11045
[2] Dusaxt P., Thesis, in: Autour de la fonction qui compte le nombre de nombres premiers (1998)
[3] Dusart P., Comptes Rendus Mathématiques de l’Académie des Sciences. La Société Royale du Canada 2 pp 53– (1999)
[4] Gordon, D. M. and Rodemich, G. ”Dense admissible sets.”. Algorithmic number theory. 3rd international symposium, ANTS–III. June21–251998, Portland, OR, USA. Edited by: Buhler, J. P. pp.216–225. Berlin: Springer. [Gordon and Rodemich 98], Proceedings., Lect. Notes Comput. Sci. 1423 · Zbl 0920.11065
[5] Hardy G. H., Acta Mathematica 44 pp 1– (1923) · JFM 48.0143.04
[6] Hensley D., Acta Arithmetica 25 pp 375– (1974)
[7] Montgomery H. L., Mathematika 20 (40) pp 119– (1973) · Zbl 0296.10023
[8] Rosser J. B., Illinois Journal of Mathematics 6 pp 64– (1962)
[9] Panaitopol L., Acta Arithmetica 94 (4) pp 373– (2000)
[10] Schinzel A., Acta Arithmetica 7 pp 1– (1961)
[11] Schinzel A., Acta Arithmetica 4 pp 185– (1958)
[12] Udrescu V., Revue Roumaine de Mathématiques Pures et Appliquées 20 pp 1201– (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.