Completely multiplicative function: Difference between revisions

Revision as of 14:32, 3 August 2011

Revision as of 02:43, 18 September 2011

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<math>f \cdot (g*h)=(f \cdot g)*(f \cdot h)</math>

where ''*'' represents the [[Dirichlet product]] and <math>\cdot</math> represents pointwise multiplication.<ref>Apostol pg. 49</ref>. One consequence of this is is that for any completely multiplicative function ''f'' one has

<math>f*f = \tau \cdot f.</math>