Dirichlet series

A Dirichlet series is a type of infinite series of the form: \[ D(s) = \sum_{n=1}^\infty \frac{a_n}{n^s} \] where \( s \) is a complex variable, \( a_n \) are complex coefficients, and \( n \) ranges over the positive integers. The series converges for certain values of the complex variable \( s \) depending on the properties of the coefficients \( a_n \).