[ANNOUNCE] Efficient Algo for Polylog and Hurwitz Zeta

[Stavros Garoufalidis]

Dear Linas,

Thank you for your interest in our polylogs paper, and your nice and 
efficient computations. In fact, I really wonder how efficiently resurgent 
functions can be computed, but this is a slightly different topic. I will 
have a closer look at your paper. A minor (stupid me!) comment: my last 
name is misspelled in your [CG] reference.

With best regards,

Stavros

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| Stavros Garoufalidis            | Phone:     (404) 894-6614           |
| School of Mathematics           | FAX:       (404) 894-4409           |
| Georgia Institute of Technology | e-mail:    stavros at math.gatech.edu  |
| Atlanta, GA  30332-0160, USA    | http://www.math.gatech.edu/~stavros |
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On Mon, 12 Feb 2007, Linas Vepstas wrote:

>
> Hi,
>
> 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.
>
> http://arxiv.org/abs/math.CA/0702243
>
> 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.
>
> --linas
>

-- 
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| Stavros Garoufalidis            | Phone:     (404) 894-6614           |
| School of Mathematics           | FAX:       (404) 894-4409           |
| Georgia Institute of Technology | e-mail:    stavros at math.gatech.edu  |
| Atlanta, GA  30332-0160, USA    | http://www.math.gatech.edu/~stavros |
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