Dirichlet Series

Definition

A Dirichlet series is a series of the form

\[ \sum_{n = 1}^\infty \frac{a_n}{n^s}\]

where \(a_n\) is a sequence of complex numbers.

Examples of Dirichlet series' include the Riemann zeta function and the Dirichlet \(L\)-function.

Dirichlet series involving many different arithmetic functions are studied in analytic number theory, including with the divisor function, von Mangoldt function and mobius function