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The Estimation of the Mertens Function

The Estimation of the Mertens Function
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摘要 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. 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.
作者 Janusz Czopik
机构地区 [
出处 《Advances in Pure Mathematics》 2019年第4期415-420,共6页 理论数学进展(英文)
关键词 Mertens FUNCTION CHEBYSHEV FUNCTIONS RIEMANN HYPOTHESIS Mertens Function Chebyshev Functions Riemann Hypothesis
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