A practical analytic method for calculating 𝜋(𝑥)

Franke, Jens; Kleinjung, Thorsten; Büthe, Jan; Jost, Alexander

doi:10.1090/mcom/3038

A practical analytic method for calculating $\pi (x)$
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by Jens Franke, Thorsten Kleinjung, Jan Büthe and Alexander Jost;

Math. Comp. 86 (2017), 2889-2909

DOI: https://doi.org/10.1090/mcom/3038

Published electronically: March 30, 2017

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Abstract:

In this paper we give a description of a practical analytic method for the computation of $\pi (x)$, the number of prime numbers $\leq x$. The method is similar to the one proposed by Lagarias and Odlyzko but uses the Weil-Barner explicit formula instead of curve integrals.

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