Re: Zeta function bug?

[Andrew John Walker <ajw01@uow.edu.au>]

On Wed, 7 Jan 2004, Karim Belabas wrote:

> * Andrew John Walker <ajw01@uow.edu.au> [2003-12-31 03:37]:
> > Thanks very much for the recent update, zeta() seems
> > to be a lot faster now. I'd like to ask someone to check
> > one value which may be producing a bad evaluation.
> >
> > Under pari Version 2.0.17 (beta)
> > ? zeta(4.45+292532.0*I)
> > %4 = 0.9628325946986762532107312785 - 0.007964269348872060270684500688*I
> >
> > Under pari Version 2.2.7 (alpha)
> > (13:13) gp > zeta(4.45+292532.0*I)
> > %77 = -1.519052693065775291998804237 E84 + 3.820179262621090164984728018
> > E84*I
> >
> > Which (if any) of these is correct?
>
> Neither. It should be
>
>   0.9628325946986762532107312786 - 0.007964269348872060270684500689*I
>
> (OK, 2.0.17 is closer :-)
>
> The problem is due to an overflow in a C long multiplication (when more than
> 46340 terms need to be summed to obtain the required precision). I have fixed
> this in CVS.
>
> I can update the Windows binary if this problem is too much of an annoyance.
>
> Thanks,
>
>     Karim.

Thanks very much Karim. I'd appreciate if the Windows version
could be updated whenever convenient. I came across the problem
while finding zeros of the "prime zeta function". I'm using
low precision for actually finding them which works ok. The
problem comes about when calculating some of them to higher
precision, say \p28, for verification. Using 2.0.17 for these
is much slower!

Andrew