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arXiv · 1907.12979

Counting Primes Rationally And Irrationally

N. A. Carella
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Abstract

The recent technique for estimating lower bounds of the prime counting function $\pi(x)=#\{p \leq x: p\text{ prime}\}$ by means of the irrationality measures $\mu(\zeta(s)) \geq 2$ of special values of the zeta function claims that $\pi(x) \gg \log \log x/\log \log \log x$. This note improves the lower bound to $\pi(x) \gg \log x$, and extends the analysis to the irrationality measures $\mu(\zeta(s)) \geq 1$ for rational ratios of zeta functions.

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N. A. Carella. 2019-07-29. Counting Primes Rationally And Irrationally. https://arxiv.org/abs/1907.12979

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