Average order of an arithmetic function: Difference between revisions

Revision as of 09:01, 18 August 2014

Revision as of 09:54, 18 August 2014

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\text{RHS}

&=\sum_{n}q^{n(1-s)}\sum_{n}(\sum_{\text{deg}(m)=n}h(m))u^{n}\\

&=\sum_{n}q^{n}u^{n}\sum_{nl}q^{nl}q^{nklk}u^{nl}\\

&=\sum_{n}(\sum_{j \mathop =0}^{n}q^{n-j}q^{jk+j})\\

&=\sum_{n}(q^{n}(\frac{1-q^{k(n+1)}}{1-q^{k}}))u^{n}