Divisor function: Difference between revisions

Revision as of 15:16, 9 October 2022

Revision as of 17:37, 30 October 2022

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:<math>\sum_{n=1}^\infty \frac{\sigma_{a}(n)}{n^s} = \zeta(s) \zeta(s-a)\quad\text{for}\quad s>1,s>a+1,</math>

whichwhere <math>\zeta</math> is the [[Riemann zeta function]]. The series for ''d''(''n'')&nbsp;=&nbsp;''&sigma;''₀(''n'') gives: {{sfnp|Hardy|Wright|2008|pp=326-328|loc=§17.5}}

: <math>\sum_{n=1}^\infty \frac{d(n)}{n^s} = \zeta^2(s)\quad\text{for}\quad s>1,</math>