Computing L-Functions of Quadratic Characters at Negative Integers

Abstract

We survey a number of different methods for computing $L(\chi ,1-k)$ for a Dirichlet character $\chi$, with particular emphasis on quadratic characters. The main conclusion is that when $k$ is not too large (for instance $k\le 100$) the best method comes from the use of Eisenstein series of half-integral weight, while when $k$ is large the best method is the use of the complete functional equation, unless the conductor of $\chi$ is really large, in which case the previous method again prevails.