Dirichlet matrices: determinants, permanents and the \textit{Factorisatio Numerorum} problem

DOI10.1016/j.laa.2021.07.006zbMath1475.15039OpenAlexW3185358151MaRDI QIDQ1979388

André Pierro de Camargo

Publication date: 2 September 2021

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

Full work available at URL: https://doi.org/10.1016/j.laa.2021.07.006

zbMATH Keywords

determinantpermanentDirichlet matrixRedheffer matrix

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Uses Software

• OEIS

Cites Work

• Matrices related to Dirichlet series
• On the spectral radius of a (0,1) matrix related to Mertens' function
• Spectral properties of a matrix of Redheffer
• The Redheffer matrix of a partially ordered set
• Factorizing matrices by Dirichlet multiplication
• Distribution of the number of factors in random ordered factorizations of integers
• The On-Line Encyclopedia of Integer Sequences
• A sparser matrix representation of the Mertens function
• On the eigenstructure of sparse matrices related to the prime number theorem
• On some asymptotic formulas in the theory of the ``factorisatio numerorum
• Elementary methods in the study of the distribution of prime numbers
• Some theorems on the permanent
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