Re: [Help-gsl] complex numbers and zeta function

[Jordi Gutiérrez Hermoso]

On 19/06/2008, Ruben Henner Zilibowitz <address@hidden> wrote:
> Ok source code is attached to this email.

Thank you. One comment: you used C complexes, which don't work in C++.
Funny, did you know that C and C++ have mutually incompatible
implementations of complex numbers, at least with gcc?

For inclusion into the GSL, the code should use gsl_complex.h so that
we don't run afoul of this C/C++ silliness. It's a trivial fix; I can
do this myself.

>  No I didn't rely on the Pari source partly because the author seems to have
> used french names for everything which I couldn't really understand.

Hm, I speak French, but I don't really know much about zeta (I plan to
fix the latter soon). Would it help if I translated the code into
English? Would you able to implement a better complex zeta algorithm
this way?

>  One caveat though: my implementation of the zeta function seems to work
> well provided the argument isn't far up the "critical strip". In such cases
> a different algorithm will need to be used and I haven't managed to figure
> out how to do that yet.

Well, here's a view of the critical strip from -100 to 100 on the
imaginary axis and 0.4 to 0.6 on the real, the absolute value of zeta
on that strip. It's with rainbow colours, so violet is small (zero)
and red is big.

     http://www.cimat.mx/~jordi/piccies/critical-line.jpg

Thank you so much for this,
- Jordi G. H.