: Mathématiques: Dirichlet series

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mathematical analysis > complex analysis > meromorphic function > L-function > Dirichlet series

Dirichlet series

In mathematics, a Dirichlet series is any series of the form
${\\displaystyle \\sum _{n=1}^{\\infty }{\ rac {a_{n}}{n^{s}}},}$
where s is complex, and ${\\displaystyle a_{n}}$ is a complex sequence. 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 Peter Gustav Lejeune Dirichlet.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Dirichlet_series)

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