Unitary Convolution and Generalized MӦbius Function

The concept of unitary convolution in the commutative ring of arithmetic functions, under the two operations of addition and unitary convolution, is investigated. A generalized unitary MӦbius function is defined and its basic properties, which extend those corresponding classical ones are derived. Of particular interest are certain generalized unitary MӦbius inversion formula and some characterizations of multiplicative functions.

Keywords: arithmetic function, Mӧbius inversion formula, multiplicative function, unitary convolution

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