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:
“His character as one of the fathers of the English language would alone make his works important, even those which have little poetical merit. He was as simple as Wordsworth in preferring his homely but vigorous Saxon tongue, when it was neglected by the court, and had not yet attained to the dignity of a literature, and rendered a similar service to his country to that which Dante rendered to Italy.”
—Henry David Thoreau (1817–1862)