On Differences of Twokth Powers: An Asymptotic Formula for the Mean-Square of the Error Term Original Research Article

The arithmetic functionr−k(n) counts the number of ways to write a natural numbernas the difference of twokth powers (kgreater-or-equal, slanted2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function ofr−k(n) leads in a natural way to a certain error termΔ−k(t). In this article we prove an asymptotic formula for the mean-square ofΔ−k(t).