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

Permanent link to this document
https://projecteuclid.org/euclid.em/1090350929

Mathematical Reviews number (MathSciNet)
MR2068888

Zentralblatt MATH identifier
1139.11317

Citation

Dokchitser, Tim. Computing Special Values of Motivic L -Functions. Experiment. Math. 13 (2004), no. 2, 137--150. https://projecteuclid.org/euclid.em/1090350929