# Contents

## Idea

$L$-functions are certain meromorphic functions generalizing the Riemann zeta function. They are typically defined by what is called an $L$-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 Dedekind zeta function for which the L-series (the Dirichlet L-function) is complicated from the classical Riemann case by the presence of the additional parameter, the Dirichlet character.

## Examples

Could not include zeta-functions and eta-functions and L-functions – table

## References

• E. Kowalski, first part of Automorphic forms, L-functions and number theory (March 12–16) Three Introductory lectures (pdf)

• D. Goldfeld, J. Hundley, chapter 2 of Automorphic Representations and L-functions for the General Linear Group, vol. 1, Cambridge University Press, 2011 (pdf)

Revised on August 21, 2014 09:47:00 by Urs Schreiber (82.113.121.235)