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Mertens conjecture : ウィキペディア英語版
Mertens conjecture

In mathematics, the Mertens conjecture is the false statement that the Mertens function ''M''(''n'') is bounded by √''n'', which implies the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes in an 1885 letter to Charles Hermite (reprinted in ) and , and disproved by .
It is a striking example of a mathematical proof contradicting a large amount of computational evidence in favor of a conjecture.
== Definition ==

In number theory, we define the Mertens function as
:M(n) = \sum_ \mu(k)
where μ(k) is the Möbius function; the Mertens conjecture is that for all ''n'' > 1,
:\left| M(n) \right| < \sqrt .\,

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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