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The Estimation of the Mertens Function
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Advances in Pure Mathematics·Volume 09 (2019)·Pages 415–420·Published 11 April 2019·DOI10.4236/apm.2019.94019
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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.
KeywordsMertens FunctionChebyshev FunctionsRiemann Hypothesis
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