Re: Zeta function bug?

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

On Tue, 30 Dec 2003, Igor Schein wrote:

> On Wed, Dec 31, 2003 at 01:27:16PM +1100, Andrew John Walker wrote:
> >
> > 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
>
> Mathematica 4.0 for IBM RISC System/6000
> Copyright 1988-1999 Wolfram Research, Inc.
>  -- Motif graphics initialized --
>
> In[1]:= Zeta[4.45+292532.0*I]
>
> Out[1]= 0.962833 - 0.00796427 I
>

Two points I missed. Firstly this can easily be checked using
the zeta(z)=suminf(n=1,1/n^z) which confirms that 2.0.17 is
giving the correct value.

Also, under 2.2.7 (alpha), using \p9 gives
0.962832595 - 0.00796426936*I
and \p18 gives -1.11638661988664799 E35 - 1.79005656904284931 E34*I

Andrew