Computing special values of motivic L-functions

Details Computing special values of motivic L-functions Computing special values of motivic L-functions

2002-07-30

arxiv.org/abs/math/0207280v1

Mathematics

Number Theory

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

Scientific paper

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).

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