Re: Zeta function bug?

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

* 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.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dep. de Mathematiques, Bat. 425   Fax: (+33) (0)1 69 15 60 19
Universite Paris-Sud              http://www.math.u-psud.fr/~belabas/ 
F-91405 Orsay (France)            http://pari.math.u-bordeaux.fr/  [PARI/GP]