Properties of rational arithmetic functions

Rational arithmetic functions are arithmetic functions of the form g1 ∗···∗ gr ∗ h−1 1 ∗ ···∗h−1 s , where gi, hj are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established; second, possible Busche-Ramanujan-type identities are investigated; third, binomial-type identities are derived; and finally, properties of the Kesava Menon norm of such functions are proved.