The character sums over the set of <i>k</i>th power residues

The primary objective of this paper is to utilize the mean value of Dirichlet L-functions, along with the properties of kth power residues and Gauss sums, to derive mean value formulas for character sums over the set of kth power residues. It is observed that the cancellation phenomenon of character sums on this set is considerably weaker than that observed over general continuous intervals.