-functions are certain meromorphic functions generalizing the Riemann zeta function. They are typically defined by what is called an -series which is then meromorphically extended to the complex plane.
Many L-functions have mutually similar deep features like satisfaction of a functional equation etc. The generalized Riemann conjecture is concerned with zeros of the Dirichlet zeta function? for which the L-series is complicated from the classical Riemann case by the presence of the additional parameter, the Dirichlet character.