An Artin L-function encodes traces of Frobenius elements in a Galois representation and converts character sums over primes into analytic information.
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The Artin L-function is a generalization of the classical Riemann zeta function and is an important object in number theory and arithmetic geometry, particularly in the context of class field theory and algebraic number theory. It is associated with a representations of a Galois group, collections of characters, and the study of L-functions in the context of number fields. ### Definition 1.