2019/07/29 by N. A. Carella, Carella, N. A.
Computer Science · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1907.12979
openalex publication_date 2019/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The recent technique for estimating lower bounds of the prime counting function π(x)=#\p ≤ x: p prime\ by means of the irrationality measures μ(ζ(s)) ≥ 2 of special values of the zeta function claims that π(x) ≫ log log x/log log log x. This note improves the lower bound to π(x) ≫ log x, and extends the analysis to the irrationality measures μ(ζ(s)) ≥ 1 for rational ratios of zeta functions.