This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# DirichletL

 DirichletL gives the Dirichlet L-function for the Dirichlet character with modulus k and index j.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• For , , where is a Dirichlet character.
• The possible Dirichlet characters modulo k are specified by an index j, and given by DirichletCharacter.
• DirichletL can be evaluated to arbitrary numerical precision for integer k and j, and arbitrary complex s.
A plot along the line :
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A plot along the line :
 Out[1]=
 Scope   (4)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
DirichletL threads element-wise over lists and matrices:
 Applications   (4)
Plot the real part of a DirichletL function on the critical line:
Plot the real part across the critical strip:
Find a zero of a DirichletL function:
Plot real and imaginary parts in the vicinity of nearby zeros:
The real part of a Dirichlet L-function:
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