## A Proof of Riemann Hypothesis Using the Growth of Mertens Function M(x)

**Authors:** Young-Mook Kang

A study of growth of M(x) as x → ∞ is one of the most useful
approach to the Riemann hypophotesis(RH). It is very known that the RH is
equivalent to which M(x) = O(x^{1/2+ε}) for ε > 0. Also Littlewood proved that
"the RH is equivalent to the statement that
lim_{x → ∞} M(x)x^{-1/2-ε} = 0, for
every ε > 0".[1] To use growth of M(x) approaches zero as x → ∞, I simply
prove that the Riemann hypothesis is valid. Now Riemann hypothesis is not
hypothesis any longer.

**Comments:** 6 pages, Submitted to annals of mathematics

**Download:** **PDF**

### Submission history

[v1] 4 Mar 2010

[v2] 5 Mar 2010

[v3] 8 Mar 2010

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