The Mertens function slowly grows in positive and negative directions both on average and in peak value, oscillating in an apparently chaotic manner passing ... Representations · As an integral · Calculation |
| Функция Мертенса |  |
Функция Мертенса — числовая функция, определяемая для натуральных чисел n формулой:
M(n) = \sum\limits_{k=1}^n \mu,
где {\displaystyle \mu } — функция Мёбиуса. Википедия
The Mertens function is the summary function M(n)=sum_(k=1)^nmu(k), where mu(n) is the Möbius function (Mertens 1897; Havil 2003, p. 208). |
It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor. |
18 февр. 2022 г. · Earlier in his career, Littlewood [1912] outlined a proof of a theorem that states criteria for the Mertens function M(x) that are equivalent to ... |
The partial sums of the Möbius function give a summatory function, the summatory Möbius function, which is called the Mertens function, named after Franz ... |
In this paper we derive new properties of Mertens function and discuss about a likely upper bound of the absolute value of the Mertens function √log(𝑥!) > |𝑀(𝑥)| ... |
25 янв. 2021 г. · We study the local properties of the Mertens function, ie its variation induced by each Möbius coefficient restricted to the square-free numbers. |
Abstract. In this paper, we prove two formulas involving Mertens and Chebyshev functions. The first formula was done by Mertens himself without a proof. |
Abstract. We describe a numerical experiment concerning the order of magnitude of {\small }, where {\small M(x) M ( x ) } is the Mertens function (the summatory ... |
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