# L-function

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

A generalization of the zeta-function at the cost of introducing characters (cf. Character of a group). The -functions form a complicated class of special functions of a complex variable, defined by a Dirichlet series or an Euler product with characters. They are the basic instrument for studying by analytic methods the arithmetic of corresponding mathematical objects: the field of rational numbers, algebraic fields, algebraic varieties over finite fields, etc. The simplest representatives of -functions are the Dirichlet -functions (cf. Dirichlet -function). The remaining -functions are more or less close analogues and generalizations of these -functions.