Substitute <math>x=q^{n}</math> the above equation becomes:
<math>D(n)=xlog_x log_{q}(x)+x</math> which resembles closely the analogous result for integers <math>\sum_{k \mathop =1}^{n}d(k)=xlogx+(2\gamma-1)x+O(\sqrt{x})</math>, where <math>\gamma</math> is [[Euler constant]].
It is ainteresting famousto problemnote inthat [[elementarynot numbera theory]]lot tois findknown about the error term.Infor the integers, while in the polynomials case, there is no error term.! This is because of the very simple nature of the zeta function <math>\zeta_{A}(s)</math>, and that it has NO zeros.
