TITLE:
The Estimation of the Mertens Function
AUTHORS:
Janusz Czopik
KEYWORDS:
Mertens Function, Chebyshev Functions, Riemann Hypothesis
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.4,
April
29,
2019
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.