Formulas for Positive, Negative and Zero Values of the Möbius Function
arXiv:0905.0294
Abstract
We obtained the formulas for the quantities of positive, negative and zero values of the Mobius function for any real x in terms of the Mobius function values for square root of x - similar to the identities we found earlier for the Mertens function [1]. Using the Dirac delta function approach [3, 2] we propose the equations showing how the Mertens and related functions can generate the output values.
5 pages