Re: Dirichlet L-Functions

[Ariel Pacetti <apacetti@math.utexas.edu>]

A stupid question (from my ignorance): I heard a talk recently by 
Guardia-Montes-Nart about a package they implemented in magma to compute 
factorization of ideals and many other number field invariants without 
computing explicitely the ring of integers (which I presume Pari does, 
right?). They posted the algorithm in arxiv

http://arxiv.org/abs/1005.4596

where they can work with quite big number fields (I suggested them to 
implement L-series computations, and answered will do), do you (experts in 
Pari) think it is worth it to have something similar implemented in GP? (I 
saw it has nothing to do with the standard way to write down ideals nor 
integers which might be a LOT of work to do, and so far I only can think 
in computing L-functions and ideal factorizations as applications).

I am just sharing my question with you all....

Ariel

On Mon, 12 Jul 2010, John Cremona wrote:

> Apologies, I gave Vladimir Dokchitser's URL instead of his brother's
> which is http://www.dpmms.cam.ac.uk/~td278/
>
> John
>
> On 12 July 2010 13:40, John Cremona <john.cremona@gmail.com> wrote:
> > Tim Dokchitser's address is now Cambridge: http://www.dpmms.cam.ac.uk/~vd209/
> >
> > Also, Jeroen Demeyer and I have just yesterday edited Dokchitser's
> > computel.gp script so that it works with version 2.4.3;  I have
> > attached the edited version here (which I sent to Tim today).
> >
> > John Cremona
> >
> > On 12 July 2010 13:04, Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr> wrote:
> > > * Charles Greathouse [2010-07-09 18:04]:
> > > > 1. Is there a good way to compute a Dirichlet L-function in Pari?  In
> > > > particular, I'd like to calculate one with chi = kronecker(D, p) and
> > > > fixed D and s.
> > >
> > > There are two "simple" ways, both available in the archive of
> > > Contributed GP scripts,
> > >
> > >  http://www.math.u-bordeaux1.fr/~belabas/pari/scripts/
> > >
> > > Specifically, item #2 (by Henri Cohen):
> > >
> > >  http://www.math.u-bordeaux1.fr/~belabas/pari/scripts/cohen.gp
> > >
> > > and #3 (by Tim Dokchitser)
> > >
> > >  http://maths.dur.ac.uk/~dma0td/computel/
> > >
> > > > 2. (Encroaching on pari-dev) If the answer to #1 is negative, and I
> > > > write a function implementing it, should I submit it for inclusion in
> > > > future versions?
> > >
> > > Pascal Molin, a student of mine, is working on a more general
> > > implementation of Dokchitser's script (with new ideas of his, as well as
> > > from Booker, Rubinstein, and others), which will be directly available
> > > in the PARI/GP package.
> > >
> > > If you devise specific improvements to script #2 above, you may send
> > > patches to me. (Script #3 is maintained directly by Tim Dokchitser.)
> > >
> > > Cheers,
> > >
> > >    K.B.
> > > --
> > > Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> > > Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
> > > 351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
> > > F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
> > > `