In mathematics, a Dirichlet series is any series of the form
where s and an 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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