Re: Dirichlet L-Functions

[Charles Greathouse <charles.greathouse@case.edu>]

Henri Cohen, in response to my original message, sent me his
Lsimpquad_c script.  It looks similar to Lquad from
http://www.math.u-bordeaux1.fr/~belabas/pari/scripts/cohen.gp ; I will
compare them, as well as Dokchitser's (presumably less similar)
script.

Since it looks like something better is coming, I won't spend too much
time converting them to C -- I'll just gp2c, type-specialize, and
glance at the inner loop.

Thanks!

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Jul 12, 2010 at 8:04 AM, 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]
> `