A series sum a(n) e^(-λ(n) z), where a(n) and z are complex and {λ(n)} is a monotonic increasing sequence of real numbers. The numbers λ(n) are called the exponents, and a(n) are called the coefficients. When λ(n) = ln n, then e^(-λ(n) z) = n^(-z), the series is a normal Dirichlet L-series. The Dirichlet series is a special case of the Laplace-Stieltjes transform.

Dirichlet generating function | Dirichlet L-series | Laplace-Stieltjes transform | modular form | modular function | zeta function

Lejeune Dirichlet