Dirichlet Series

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Dirichlet series

[‚dē·rē′klā ‚sir·ēz]
A series whose n th term is a complex number divided by n to the z th power.

Dirichlet Series


(named for P. G. L. Dirichlet), series of the form

where the an are constants and s = σ + it is a complex variable. For example, the series

represents the zeta function for σ > 1. The theory of Dirichlet series originally arose under the strong influence of analytic number theory. Eventually it developed into an extensive branch in the theory of analytic functions.