Editing Arithmetic function (section)

=== ''τ''(''n'') – Ramanujan tau function ===
'''[[Ramanujan tau function|''τ''(''n'')]]''', the Ramanujan tau function, is defined by its [[generating function]] identity:
<math display="block">\sum_{n\geq 1}\tau(n)q^n=q\prod_{n\geq 1}(1-q^n)^{24}.</math>

Although it is hard to say exactly what "arithmetical property of ''n''" it "expresses",<ref>Hardy, ''Ramanujan'', § 10.2</ref> (''τ''(''n'') is (2''π'')<sup>−12</sup> times the ''n''th Fourier coefficient in the [[q-expansion|''q''-expansion]] of the [[Modular discriminant#Modular discriminant|modular discriminant]] function)<ref>Apostol, ''Modular Functions ...'', § 1.15, Ch. 4, and ch. 6</ref> it is included among the arithmetical functions because it is multiplicative and it occurs in identities involving certain ''σ''<sub>''k''</sub>(''n'') and ''r''<sub>''k''</sub>(''n'') functions (because these are also coefficients in the expansion of [[modular form]]s).