Number Theory


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(x1/2+ε) for ε > 0. Also Littlewood proved that "the RH is equivalent to the statement that limx → ∞ 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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