## 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

**Unique-IP document downloads:** 1927 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*