In mathematics, a **Dirichlet series** is any series of the form

where *s* and *a*_{n} are complex numbers and *n* = 1, 2, 3, ... . It is a special case of general Dirichlet series.

Dirichlet series play a variety of important roles in analytic number theory. The most usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named in honor of Johann Peter Gustav Lejeune Dirichlet.

Read more about Dirichlet Series: Combinatorial Importance, Examples, Formal Dirichlet Series, Analytic Properties of Dirichlet Series: The Abscissa of Convergence, Derivatives, Products, Integral Transforms, Relation To Power Series

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