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Volume 10, Issue 3, Article 62 |
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A Matrix Inequality for Möbius Functions
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Authors: |
Olivier Bordellčs, Benoit Cloitre, |
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Keywords:
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Determinants, Dirichlet convolution, Möbius functions, Singular values. |
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Date Received:
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24/11/2008 |
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Date Accepted:
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27/03/2009 |
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Subject Codes: |
15A15, 11A25, 15A18, 11C20.
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Editors: |
László Tóth, |
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Abstract: |
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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