The explicit expression for the two-body n-dimensional Coulomb Green's func
tion is presented in the Schwinger's integral form. The structure of its si
ngularities is found to be independent on n. This fact leads to the Peterko
p's theory of effective charges as well as to the new method of removing th
ree-body Coulomb singularities. The bound states problem for the n-dimensio
nal Coulomb potential is investigated too.