We present an algorithm to compute values L(s) and derivatives {\small $L^{(k)}(s)$} of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose {\small $\Gamma$}-factor is of the form {\small $A^s\prod_{i=1}^d \Gamma(\frac{s+\lambda_j}{2})$} with d arbitrary and complex {\small $\lambda_j$}, not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).
@article{1090350929,
author = {Dokchitser, Tim},
title = {Computing Special Values of Motivic L-Functions},
journal = {Experiment. Math.},
volume = {13},
number = {1},
year = {2004},
pages = { 137-150},
language = {en},
url = {http://dml.mathdoc.fr/item/1090350929}
}
Dokchitser, Tim. Computing Special Values of Motivic L-Functions. Experiment. Math., Tome 13 (2004) no. 1, pp. 137-150. http://gdmltest.u-ga.fr/item/1090350929/