L-function

right|thumb|300px|The Riemann zeta function can be thought of as the archetype for all L-functions.

In mathematics, an '''L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series' is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an example of an L-function, and some important conjectures involving L-functions are the Riemann hypothesis and its generalizations.