László Tóth: Expansions of arithmetic functions of several variables with respect
to certain modified unitary Ramanujan sums, 213-223

Abstract:

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

Key Words: Ramanujan expansion of arithmetic functions, arithmetic function of several variables, multiplicative function, unitary divisor, sum of unitary divisors, unitary Euler function, unitary Ramanujan sum.

2010 Mathematics Subject Classification: Primary 11A25. Secondary 11N37