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
Famous quotes containing the word series:
“The womans world ... is shown as a series of limited spaces, with the woman struggling to get free of them. The struggle is what the film is about; what is struggled against is the limited space itself. Consequently, to make its point, the film has to deny itself and suggest it was the struggle that was wrong, not the space.”
—Jeanine Basinger (b. 1936)