The Mertens Function and The Proof of The Riemann’s Hypothesis
M. Sghiar, Allée Capitaine J. B Bossu, 21240, Talant, France.
Manuscript received on 10 December 2017 | Revised Manuscript received on 18 December 2017 | Manuscript Published on 30 December 2017 | PP: 144-145 | Volume-7 Issue-2, December 2017 | Retrieval Number: B5267127217/17©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: I will prove that M (n)= O(n 1/ 2+ϵ) where M is the Mertens function, and I deduce a new proof of the Riemann’s hypothesis.
Keywords: Prime Number, Number Theory , Distribution Of Prime Numbers, The Law Of Prime Numbers, The Riemann Hypothesis, The Riemann Zeta Function, The Mertens Function.
Scope of the Article: Database Theory and Application