8 июл. 2017 г. · The fact that the Riemann Hypothesis and the Mobius function are related has its origin in the formula 1ζ(s)=∞∑n=1μ(n)n−s.

22 мая 2018 г. · For the reciprocal of Riemann zeta function 1ζ(s), an=μ(n). RH conjectures that the series converges for ℜ(s)>12.

5 мар. 2016 г. · the generalized Riemann hypothesis is for Dirichlet characters χ. a Dirichlet character is multiplicative χ(nm)=χ(n)χ(m) and periodic ...

20 янв. 2019 г. · The Mertens function M(x) is defined as |∑n≤xμ(n)|, where μ denotes the Mobius function. If χ is a primitive character modulo q, ...

26 янв. 2024 г. · Where μ is the Möbius function. Littlewood proved that if M(x)=ox(x12+ε) for every ε>0 then Riemann Hypothesis follows.

15 авг. 2015 г. · Let μ(n) denote the Mobius function, let λ(n) denote the Liouville function, and let M(x)=∑n≤xμ(n) and L(x)=∑n≤xλ(n) denote their summatory ...

19 окт. 2022 г. · More specifically, the statement that M(x)=O(xα+ε) will be equivalent to ζ(s) is free of zeros in ℜ(s)≥α.

24 июн. 2023 г. · The prime number theorem is equivalent to the fact that the nontrivial zeros of the zeta function lie in the interior of the critical strip.

16 мар. 2023 г. · Let G(x)=∑k≤xμ(k)k, where μ is the Mobius function. From this question and its answer, its mention the Riemann hypothesis is equivalent to G(x)= ...

22 сент. 2015 г. · The connections between the Liouville function and the Riemann Hypothesis were explored by Landau in his doctoral thesis of 1899.