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Irrationality measure and lower bounds for pi(x)

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Publication:4630925

zbMATH Open1432.11091arXiv0709.2184MaRDI QIDQ4630925

Author name not available (Why is that?)

Publication date: 23 April 2019

Abstract: In this note we show how the irrationality measure of zeta(s)=pi2/6 can be used to obtain explicit lower bounds for pi(x). We analyze the key ingredients of the proof of the finiteness of the irrationality measure, and show how to obtain good lower bounds for pi(x) from these arguments as well. While versions of some of the results here have been done by other authors, our arguments are more elementary and yield a lower bound of order x/logx as a natural boundary.


Full work available at URL: https://arxiv.org/abs/0709.2184



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