Ariel Pacetti on Mon, 12 Jul 2010 21:07:58 +0200 |
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Re: Dirichlet L-Functions |
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/1005.4596where 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] `