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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 : where μ(k) is the Möbius function; the Mertens conjecture is that for all ''n'' > 1, :
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