## Experimental Mathematics

### Computing Special Values of Motivic L-Functions

Tim Dokchitser

#### Abstract

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 information

Source
Experiment. Math., Volume 13, Issue 2 (2004), 137-150.

Dates
First available in Project Euclid: 20 July 2004