Year: 2019
Type: preprint
Abstract: The recent technique for estimating lower bounds of the prime counting function $π(x)=#\{p \leq x: p\text{ prime}\}$ by means of the irrationality measures $μ(ζ(s)) \geq 2$ of special values of the zeta function claims that $π(x) \gg \log \log x/\log \log \log x$. This note improves the lower bound to $π(x) \gg \log x$, and extends the analysis to the irrationality measures $μ(ζ(s)) \geq 1$ for rational ratios of zeta functions.
Source: arXiv (Cornell University)
Author: Carella, N. A.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2964406866