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
$$| \sum_{n=1}^{\infty} \frac{(-i)^{Ω(n)}}{n^2}|=\frac{π^{5}}{105}$$,
where Ω(n) counts, with multiplicity, the number of prime factors of n, and
$$| \sum_{n=1}^{\infty} \frac{(1+i)^{ω(n)}}{n^2}|^{2}=\frac{35}{12}$$,
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.