[ANNOUNCE] Efficient Algo for Polylog and Hurwitz Zeta

Linas Vepstas linas at austin.ibm.com
Mon Feb 12 19:16:47 CET 2007


I've just posted a paper describing an efficient algorithm for
computing the (classical, fractional) polylogarithm Li_s(z)
for arbitrary complex values of s and z; and similarly for the
the Hurwitz zeta function.


The algorithm generalizes Borwein's "An Efficient Algorithm for
the Riemann zeta function", and, draws on Cohen, Villegas and
Zagier "Convergence Acceleration for Alternating Series" to
propose a way of accelerating general oscillatory series.

The paper also provides a low-brow review of the monodromy of
the polylogarithm, as there does not appear to be any simple
discussion in the literature.

The algo is implemented in GMP, and the source code is available
upon request, under the LGPL license.


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