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The generating function of the Möbius function is the inverse of the zeta function:
<math display="block">\zeta(s)\,\sum_{n=1}^\infty\frac{\mu(n)}{n^s}=1, \;\;\Re s >
Consider two arithmetic functions ''a'' and ''b'' and their respective generating functions ''F''<sub>''a''</sub>(''s'') and ''F''<sub>''b''</sub>(''s''). The product ''F''<sub>''a''</sub>(''s'')''F''<sub>''b''</sub>(''s'') can be computed as follows:
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