Dirichlet L-function

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A Dirichlet L-function is a meromorphic function obtained as the analytic continuation of the Dirichlet series of the Dirichlet character.

The corresponding Dirichlet series is termed a Dirichlet L-series, and the Dirichlet L-series as well as the function are denoted where is the character and is the argument.


where is the set of all prime numbers. The equality follows from the Euler product formula.