The Estimation of the Mertens Function - Advances in Pure Mathematics

APM > Vol.9 No.4, April 2019

Advances in Pure Mathematics

Volume 9, Issue 4 (April 2019)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

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The Estimation of the Mertens Function ()

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DOI: 10.4236/apm.2019.94019 1,099 Downloads 1,900 Views Citations

Author(s)

Janusz Czopik

Affiliation(s)

2715 Cane Field Dr, Sugar Land, TX, USA.

ABSTRACT

In this paper, we prove two formulas involving Mertens and Chebyshev functions. The first formula was done by Mertens himself without a proof. The second formula is a new one. Using these formulas, we estimate the Mertens function in such manner that we obtain a sufficient condition to approve the Riemann hypothesis.

KEYWORDS

Mertens Function, Chebyshev Functions, Riemann Hypothesis

Share and Cite:

Czopik, J. (2019) The Estimation of the Mertens Function. Advances in Pure Mathematics, 9, 415-420. doi: 10.4236/apm.2019.94019.

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