Another estimating the absolute value of Mertens function

2020/10/23 by Rong Wei, Rong Qiang Wei, Wei, Rong Qiang
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications #math.GM

paper · pdf · doi:10.48550/arxiv.2010.14232

11 pages, no figures

arxiv created 2020/10/23 · openalex publication_date 2020/10/23 · arxiv updated 2020/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Through an inversion approach, we suggest a possible estimation for the absolute value of Mertens function \vert M(x) \vert that \vert M(x) \vert ∼ [(1)/(π√(ε)(x+ε))]√(x) (where x is an appropriately large real number, and ε (0<ε<1) is a small real number which makes 2x+ε to be an integer). For any large x, we can always find an ε, so that \vert M(x) \vert < [(1)/(π√(ε)(x+ε))]√(x).

Citations

• Computing the Mertens function on a GPU

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