Unital Sums of the Möbius and Mertens Functions
Madison, WI 53711
We use standard techniques of linear algebra to construct an infinite
family of identities that involve finite weighted sums of the Möbius
and Mertens functions, where the weights are equal to −1, 0, or 1. In
a related manner, we construct, for each positive integer n,
an n × n symmetric unimodular matrix,
and each matrix is used to express an
identity that involves a finite weighted sum of the Möbius function. We
establish several results on the spectral decomposition of these matrices.
Full version: pdf,
(Concerned with sequences
Received September 21 2019; revised versions received September 22 2019; December 29
2019; July 7 2020.
Published in Journal of Integer Sequences,
August 7 2020.
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