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  Volume 10, Issue 3, Article 62
A Matrix Inequality for Möbius Functions

    Authors: Olivier Bordellčs, Benoit Cloitre,  
    Keywords: Determinants, Dirichlet convolution, Möbius functions, Singular values.  
    Date Received: 24/11/2008  
    Date Accepted: 27/03/2009  
    Subject Codes:

15A15, 11A25, 15A18, 11C20.

    Editors: László Tóth,  

The aim of this note is the study of an integer matrix whose determinant is related to the Möbius function. We derive a number-theoretic inequality involving sums of a certain class of Möbius functions and obtain a sufficient condition for the Riemann hypothesis depending on an integer triangular matrix. We also provide an alternative proof of Redheffer's theorem based upon a LU decomposition of the Redheffer's matrix.

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