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Computing $\pi(x)$ Analytically

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arxiv 1203.5712 v3 pith:FEXQJA5S submitted 2012-03-26 math.NT

David J. Platt This is my paper · ORCID
classification math.NT
keywords analyticanalyticallycomputecomputingcountingdescribeevaluatefunction
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abstract

We describe a rigorous implementation of the Lagarias and Odlyzko Analytic Method to evaluate the prime counting function and its use to compute unconditionally the number of primes less than $10^{24}$.

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Cited by 1 Pith paper

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  1. Unimodular Fake Mobius Functions

    math.NT 2025-12 conditional novelty 7.0 of 10

    For multiplicative functions generated by a fixed sequence of prime-power values, an explicit formula extracts the critical-line contributions of ζ(s)^z ζ(2s)^w and gives a criterion for persistent, apparent, or absent bias.

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