The K-th Power Sum Functions Of GCD And LCM

In the first chapter of this paper, we introduce the definition of greatest common divisor, lowest common multiple, multiplicative function, Dirichlet product, Dirichlet series, Riemann zata function, Euler's identity and so on. In the second one, we improved the error termof asymptotic formula for (?)(i,j), and we also give the asymptotic formulas for sum functions (?)(i,j)~k (k > 0 and k≠1) and (?)[i,j]~k(k > 0).