The Lcm-sum Function

In the first chapter of this paper, we introduce the multiplicative function , Dirichlet product , Abel's identity ,Dirichlet series, Riemann zeta function and so on . And in the second one ,we consider the lcm-sumfunction Dirichlet series has a compact representa-tion in terms of the Riemann zeta function, asymptotic forms for values of partial sums of the Dirichlet series at real values are derived , including estimates for error terms.