Bordered Hermitian matrices and sums of the Möbius function

DOI10.1016/j.laa.2019.12.004zbMath1440.15006OpenAlexW2992365746MaRDI QIDQ2174446

Jeffery Kline

Publication date: 21 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.laa.2019.12.004

zbMATH Keywords

Möbius functionprime number theorempolytopeRiemann hypothesisHermitian matrixbordered matrixMertens function

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Asymptotic results on arithmetic functions (11N37) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Matrices, determinants in number theory (11C20)

Cites Work

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• Matrices related to Dirichlet series
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• Riemann's hypothesis as an eigenvalue problem
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• The Redheffer matrix of a partially ordered set
• A sparser matrix representation of the Mertens function
• On the eigenstructure of sparse matrices related to the prime number theorem
• Disproof of the Mertens conjecture.
• Computations of the Mertens function and improved bounds on the Mertens conjecture
• Some assertions equivalent to the prime number theorem for arithmetic progressions
• On Two Conjectures in the Theory of Numbers

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