Hi dear researchers. I published a short proof that proposes a new upper bound of the Mertens function. I used my Diophantine inequality. I really hope that my proof be useful for mathematicians who try to prove many problems by using upper bound such as the Millenium problem of Riemann hypothesis. Check my article out and give me your feedback, here is the link:
https://www.researchgate.net/publication/388324100_A_proof_of_the_Riemann_Hypothesis_by_proving_the_Generalized_Mertens_conjecture