An upper bound for the \(\ell_p\) norm of a gcd-related matrix

DOI10.1155/JIA/2006/25020zbMath1096.15009WikidataQ59212868 ScholiaQ59212868MaRDI QIDQ2491548

Pentti Haukkanen

Publication date: 29 May 2006

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/126421

zbMATH Keywords

Riemann zeta functionupper boundgreatest common divisorleast common multiple\(l_p\)-norm

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Matrices of integers (15B36) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Matrices, determinants in number theory (11C20)

Related Items (5)

Spectral asymptotics for a family of LCM matrices ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ Inertia, positive definiteness and \(\ell_p\) norm of GCD and LCM matrices and their unitary analogs ⋮ On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture ⋮ A topological approach to divisibility of arithmetical functions and GCD matrices

Cites Work

• Introduction to arithmetical functions
• Matrices associated with classes of arithmetical functions
• On Smith's determinant
• On meet and join matrices associated with incidence functions.
• Gcd-closed sets and determinants of matrices associated with arithmetical functions
• Some analogues of smith's determinant
• A note on bounds for norms of the reciprocal LCM matrix
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