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