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stale tag, most specific formulas have inline footnotes, and general references do suffice for most of this |
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for arbitrary [[complex number|complex]] |''q''| ≤ 1 and ''a''. This summation also appears as the [[Eisenstein series#Fourier series|Fourier series of the Eisenstein series]] and the [[Weierstrass elliptic functions#Invariants|invariants of the Weierstrass elliptic functions]].
For <math>k>0</math>,
:<math>\sigma_k(n) = \zeta(k+1)n^k\sum_{m=1}^\infty \frac {c_m(n)}{m^{k+1}}.</math>
The computation of the first terms of <math>c_m(n)</math> shows its oscillations around the "average value" <math>\zeta(k+1)n^k</math>:
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