Dirichlet series

A Dirichlet series is a special type of infinite sum used in mathematics, often in number theory. It has the form \(\sum_{n=1}^\infty a(n)/n^s\), where \(a(n)\) are coefficients and \(s\) is a complex number. Think of it as a blend of an infinite series and a frequency analysis, with each term related to the size of \(n\) and the value of \(a(n)\). These series help mathematicians study properties of numbers, like prime distributions and functions, by analyzing how the sum behaves as \(s\) varies.