Dirichlet series

A Dirichlet series is a series of the form

\sum_{n = 1}^{\infty} \frac{a_{n}}{n^{s}} .

Example: $a_{n} = 1$ gives the Riemann zeta function $ζ (s)$ .

Relation to Fourier series

See Fourier, Laplace and Dirichlet relationship. Summary: a Dirichlet series is the Mellin transform of the integer Dirac comb $\sum_{n} a_{n} δ (x - n)$ .