Re: Dirichlet L-Functions

[Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>]

* 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]
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