It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor. The graph shows the ... Definition · Disproof of the conjecture · References |
| Гипотеза Мертенса |  |
Гипотеза Ме́ртенса — отвергнутая математическая гипотеза, согласно которой функция Мертенса ограничена. Выдвинута Стилтьесом в 1885 году в письме Эрмиту, независимо предложена Францем Мертенсом в 1897 году. Особый интерес к гипотезе был связан с... Википедия
The Mertens conjecture was proved false by Odlyzko and te Riele (1985). Their proof is indirect and does not produce a specific counterexample. |
What did raise overwhelming skepticism about the truth of the Mertens conjecture was a series of completely unexpected results about the zeros of the zeta ... |
The Mertens conjecture states that M(x) < x 1 /2 for all x > 1, where M(x) = n x S (n) , and (n) is the Mo .. bius function. This conjecture has attracted a ... |
8 апр. 2015 г. · The truth of the Mertens conjecture implies the truth of the Riemann hypothesis and the simplicity of the complex zeros of the Riemann zeta ... |
Videolar The Mertens conjecture that |M(x)|/\sqrt{x}<1 for all x>1 was disproved in 1985 by Odlyzko and te Riele [13]. In the present paper, the known lower bound 1.06 ... |
A detailed calculation is made of the elastic energy of a straight dislocation in a cubic or hexagonal crystal, for various orientations in the crystal of the ... |
The Mertens conjecture states that |M(x)|x−1/2 < 1 for x > 1, where M(x) = ∑ 1≤n≤x μ(n) and where μ(n) is the Möbius function defined by: μ(1) = 1, ... |
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