Average order of an arithmetic function: Difference between revisions

Revision as of 09:54, 18 August 2014

Revision as of 09:56, 18 August 2014

Line 265:

<math>\sum_{\text{deg}(m)=n, m \text{ monic}} \sigma_k(m)=x^{k+1}(\frac{\zeta(k+1)}{\zeta(kn+k+1)})</math>,

which resembles closely the analogous result for the integers:

<math>\sum_{n\le x}\sigma_{k}(n)=\frac{\zeta(k+1)}{k+1}x^{k+1}+O(x^{k})</math>