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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“In the order of literature, as in others, there is no act that is not the coronation of an infinite series of causes and the source of an infinite series of effects.”
—Jorge Luis Borges (1899–1986)