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Mertens sums requiring fewer values of the Möbius function. (English) Zbl 1441.15006

An extension of the Mertens function is presented. The authors establish an identity which, for a particular case, can be established in terms of a certain matrix. For that matrix, several spectral considerations are provided.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
11A25 Arithmetic functions; related numbers; inversion formulas
11C20 Matrices, determinants in number theory
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses

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References:

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