Average order of an arithmetic function: Difference between revisions

Revision as of 06:29, 10 August 2014

Revision as of 06:31, 10 August 2014

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Substitute <math>q^{-s}=u</math> we get,

<math>\text{LHS}=\sum_{n}(\sum_{\text{deg}(m)=n} \sigma_k(m))u^{n}</math>, and by [[Cauchy product]] we get,

<math>\text{RHS}=\sum_{n}(q^{n}(\frac{1-q^{k(n+1)}}{1-q^{k}}))u^{n}</math>.