is the count of square-free integers up to x that have an even number of prime factors, minus the count of those that have an odd number. |
The Mertens function is the summary function M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function (Mertens 1897; Havil 2003, p. 208). |
| 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
In mathematics, the Mertens conjecture is the statement that the Mertens function M ( n ) {\displaystyle M(n)} {\displaystyle M(n)} ... |
18 февр. 2022 г. · = −1 if n is square-free and has an odd number of primes. The Mertens function is of great interest because of its relation to the zeta. |
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 ... |
26 окт. 2016 г. · Abstract:The Mertens function is defined as M(x) = \sum_{n \leq x} \mu(n), where \mu(n) is the Möbius function. The Mertens conjecture ... |
25 апр. 2018 г. · The purpose of this paper is to prove this conjecture and to deduce a new proof of Riemann's hypothesis. Recall also that in [7] it has been ... |
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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