Peter G. Brown, "The Modified Mobius Function," WSEAS Transactions on Computers, vol. 12, pp. -, 2013, DOI:
Peter G. Brown. The Modified Mobius Function.
WSEAS Transactions on Computers. 2013;12:-.
WSEAS Transactions on Computers
Print ISSN: 1109-2750, E-ISSN: 2224-2872
Volume 12, 2013
The Modified Mobius Function
Author:
Abstract: The Mobius function µ(n) arises naturally in Number Theory when one inverts the classical Riemann Zeta function. In my paper Modifying Mobius [1], I modified the classical Mobius function and produced a number of interesting results such as<br>
$$| \sum_{n=1}^{\infty} \frac{(-i)^{Ω(n)}}{n^2}|=\frac{π^{5}}{105}$$,
where Ω(n) counts, with multiplicity, the number of prime factors of n, and<br>
$$| \sum_{n=1}^{\infty} \frac{(1+i)^{ω(n)}}{n^2}|^{2}=\frac{35}{12}$$,
where ω(n) counts the number of distinct prime factors of n.
In this paper, I present some further arithmetic and analytic results based on these ideas.
Pages: - WSEAS Transactions on Computers, ISSN / E-ISSN: 1109-2750 / 2224-2872, Volume 12, 2013DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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