Algebraic Properties of Convolution of Arithmetic Functions on the Partial Sub-Basic Sequence of Square-Free Odd Integers

Abstract

In this paper, we introduce the notion of partial sub-basic sequence on the sub set of square-free odd integers and using convolution definition of arithmetic functions from the set of square free positive integers to real numbers and obtain some basic algebraic properties of convolution. We also define partial multiplicative functions with respect to partial basic sequences and obtain their properties. These results are extended the results given in Sridevi [7] relating to the arithmetic functions, thus this paper is a sequel to Sridevi [7].