Riemann's hypothesis as an eigenvalue problem. II

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We continue the investigations concerning the eigenvalues λ1,...,λN-1 of a certain matrix AN over the integers. On one side they permit an equivalent formulation of Riemann's hypothesis, and on the other side they are fairly uniformly distributed-with some characteristic exceptions. Section 1 contains arithmetic properties of the characteristics polynomial χN(x) of AN and in particular the examination of χN(x) at x=1, which leads to a multiplicative function ρ{variant} similar to the Möbius function μ. Section 2 gives estimates for the large eigenvalues of AN and for the power sums of all eigenvalues.

Original languageEnglish
Pages (from-to)45-73
Number of pages29
JournalLinear Algebra and Its Applications
Issue numberC
StatePublished - Jul 1987


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