M\"obius functions of higher rank and Dirichlet series
Number Theory
2021-08-05 v1
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 -free numbers. For the proof, the Riemann zeta function and cyclotomic polynomials play a key role.
Keywords
Cite
@article{arxiv.2108.01822,
title = {M\"obius functions of higher rank and Dirichlet series},
author = {Masato Kobayashi},
journal= {arXiv preprint arXiv:2108.01822},
year = {2021}
}
Comments
17 pages