A certain note about the geometry of the first counting function graph

Authors

DOI:

https://doi.org/10.5604/01.3001.0010.8001

Keywords:

prime numbers, function counting the prime numbers, Riemann’s hypothesis

Abstract

The envelope convex subtraction of the first counting function x→π(x) is a convex set delimited from the top by a graph with a certain piece of the linear function x→ϵ(x). The vertices of this set (broken nodes) form an infinite series of points (e_k,π(e_k))_1^∞. In this paper we will present some observations on the sequence (e_k )_1^∞ suggested by the 2500 collection of its initial words.

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D. Goldfeld, The Elementary Proof of the Prime Number Theorem: An Historical Perspective, https://people.math.osu.edu/nevai.1/AT/ERDOS/ErdosSelbergDispute.pdf   Google Scholar

H. L. Montgomery, S. Wagon, The Mathematical Intelligencer, 2006, 28:3, 6-9.   Google Scholar

A. M. Odlyzko, H. J. J. te Riele, Journal für die reine und angewandte Mathematik, 1985, 357, 138-160.   Google Scholar

C. Pommerance, Mathematics of Computations, 1979, 33, 399-408.   Google Scholar

Y. Zhang, Annals of Mathematics, 2014, 179, 1121-1174.   Google Scholar

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Published

2017-10-11

How to Cite

Tutaj, E. (2017). A certain note about the geometry of the first counting function graph. Science, Technology and Innovation, 4(3), 55–77. https://doi.org/10.5604/01.3001.0010.8001

Issue

Vol. 4 No. 3 (2017): Tarnow Scientific Colloquia: Technical and exact sciences

Section

Original articles

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Copyright (c) 2017 University of Applied Sciences in Tarnow, Poland & Author

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.