Re: idea 1 for Besançon atelier

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Oct 06, 2017 at 09:59:00PM +0200, Vincent Delecroix wrote:
> Dear pari devs,
> 
> Here is one thing I would like to investigate and in which PARI/GP (or their
> developers) might be of some help.
> 
> I got interested in some generalizations of multiple zeta values (and
> relations between them). My sums look like
> 
>  sum_{h1, h2, ..., hm}  1 / L1(h) L2(h) ... Lm(h)
> 
> where
>  * the sum is over all positive integers h1, ..., hm
>  * Li(h) are linear with coefficients 0 or 1
> 
> Example of such things are the multiple zeta values as
> 
> zeta(s1, ..., sm) =
>     sum 1 / (h1^s1 (h1 + h2)^s2 ... (h1 + ... + hm)^sm)

If all the Li are equal, then the result is a linear combination
of zeta values.

Cheers,
Bill.