Dirichlet Character
In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of . Dirichlet characters are used to define Dirichlet L-functions, which are meromorphic functions with a variety of interesting analytic properties. If is a Dirichlet character, one defines its Dirichlet L-series by
where s is a complex number with real part > 1. By analytic continuation, this function can be extended to a meromorphic function on the whole complex plane. Dirichlet L-functions are generalizations of the Riemann zeta-function and appear prominently in the generalized Riemann hypothesis.
Dirichlet characters are named in honour of Johann Peter Gustav Lejeune Dirichlet.
Read more about Dirichlet Character: Axiomatic Definition, Construction Via Residue Classes, A Few Character Tables, Examples, Primitive Characters and Conductor, Character Orthogonality, History
Famous quotes containing the word character:
“If you will think about what you ought to do for other people, your character will take care of itself. Character is a by-product, and any man who devotes himself to its cultivation in his own case will become a selfish prig.”
—Woodrow Wilson (1856–1924)