Computing special values of motivic L-functions

Abstract

We present an algorithm to compute values L(s) and derivatives of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Gamma-factor is a product of any number of Gamma-functions Gamma((s+l(j))/2) with complex l(j), not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).

19 pages (LaTeX), for PARI implementation and examples see http://maths.dur.ac.uk/~dma0td/computel/