On the eigenstructure of sparse matrices related to the prime number theorem

DOI10.1016/j.laa.2019.09.022zbMath1427.15014OpenAlexW2976730316WikidataQ127197309 ScholiaQ127197309MaRDI QIDQ2332445

Jeffery Kline

Publication date: 4 November 2019

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

Full work available at URL: https://doi.org/10.1016/j.laa.2019.09.022

zbMATH Keywords

prime number theoremsparse matrixDirichlet convolutionMertens functionRedheffer matrix

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Eigenvalues, singular values, and eigenvectors (15A18) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Primes (11A41)

Related Items

Bordered Hermitian matrices and sums of the Möbius function, Dirichlet matrices: determinants, permanents and the \textit{Factorisatio Numerorum} problem

Uses Software

• OEIS

Cites Work

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• Matrices related to Dirichlet series
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• A sparser matrix representation of the Mertens function
• Approximate formulas for some functions of prime numbers
• Some assertions equivalent to the prime number theorem for arithmetic progressions
• A Simple Proof of a Theorem of Landau