Formulas for Positive, Negative and Zero Values of the Möbius Function

2009/05/04 by R. M. Abrarov, Abrarov, R. M., Sanjar M. Abrarov +1 · 1 citation
Mathematics · Physics and Astronomy · #11A41 #11N05 #Advanced Mathematical Theories and Applications #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0905.0294

openalex publication_date 2009/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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