Divisor Function - Series Relations

Series Relations

Two Dirichlet series involving the divisor function are:

which for d(n) = σ₀(n) gives

and

A Lambert series involving the divisor function is:

for arbitrary complex |q| ≤ 1 and a. This summation also appears as the Fourier series of the Eisenstein series and the invariants of the Weierstrass elliptic functions.