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arXiv · 2108.01822

M\"obius functions of higher rank and Dirichlet series

Masato Kobayashi
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Abstract

We introduce M\"obius functions of higher rank, a new class of arithmetic functions so that the classical M\"obius function is of rank 2. With this idea, we evaluate Dirichlet series on the sum of the reciprocal square of all $r$-free numbers. For the proof, the Riemann zeta function and cyclotomic polynomials play a key role.

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Masato Kobayashi. 2021-08-04. M\"obius functions of higher rank and Dirichlet series. https://arxiv.org/abs/2108.01822

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