Multiple divisor chains and determinants of matrices associated with completely even functions (modr)

DOI10.1080/03081087.2013.818993zbMath1307.11035OpenAlexW1995925455MaRDI QIDQ2926021

Shuangnian Hu, Shao-Fang Hong

Publication date: 29 October 2014

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2013.818993

zbMATH Keywords

determinantdivisibilitymultiplicative functiongcd matrixSmith matrixlcm matrixmultiple divisor chain

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Arithmetic functions; related numbers; inversion formulas (11A25) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (5)

Determinants of matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ Hyperdeterminants on meet-semilattices ⋮ Divisibility among power matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions ⋮ Further results on generalized LCM matrices

Cites Work

• Nonsingularity of matrices associated with classes of arithmetical functions
• Matrices associated with classes of arithmetical functions
• Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains
• Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains
• Divisibility properties of power GCD matrices and power LCM matrices
• Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets
• Arithmetical properties of generalized Ramanujan sums
• Gcd-closed sets and determinants of matrices associated with arithmetical functions
• Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains
• Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains II
• ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r)
• A CLASS OF ARITHMETICAL FUNCTIONS
• Arithmetical Inversion Formulas
• Determinants of multiplicative Toeplitz matrices
• Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains
• Power GCD Matrices for a UFD
• A Generalization of Smith's Determinant
• Matrices associated with arithmetical functions
• Factorization of matrices associated with classes of arithmetical functions
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES
• Divisibility properties of Smith matrices
• Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets

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