Expansions of arithmetic functions of several variables with respect to certain modified unitary Ramanujan sums

Abstract

We introduce new analogues of the Ramanujan sums, denoted by ${\tilde{c}}_q(n)$, associated with unitary divisors, and obtain results concerning the expansions of arithmetic functions of several variables with respect to the sums ${\tilde{c}}_q(n)$. We apply these results to certain functions associated with ${\sigma }^{\ast }(n)$ and ${\varphi }^{\ast }(n)$, representing the unitary sigma function and unitary phi function, respectively.

11 pages, 1 table, revised. arXiv admin note: text overlap with arXiv:1704.02881

References in corpus (1)

• Ramanujan expansions of arithmetic functions of several variables