Re: Question on finding a Riemann Zeta function zero for high values of s

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Oct 22, 2025 at 04:07:08PM -0700, American Citizen wrote:
> Hmm.. I am encountering problems after patching and recompiling.
> 
> I am unable to do the 10^21 value that Odlyzko gave as
> 
> s = 1/2 +  1370919909931995308226.68016095*I
> 
> the gp pari program hangs.

Does it hang or is it just really slow ?
For reference on a 20 core system:

?  \p19
   realprecision = 19 significant digits
? for(i=1,22,gettime();print(i,":",zeta(1/2 +  I*10^i),":",gettime))
1:1.544895220296752767-0.1153364652712733754*I:1
2:2.692619885681324091-0.02038602960259816177*I:0
3:0.3563343671943960551+0.9319978312329936651*I:2
4:-0.3393738016850152003-0.03709150586895935008*I:6
5:1.073310050874044230+5.782346434526893092*I:5
6:0.07589322974558213214+2.797882257529005767*I:6
7:11.44928615633073319-8.636833255153135178*I:7
8:-3.356950787107378080+1.404770337735806700*I:11
9:-2.764920304963509697-1.679439111325650030*I:38
10:0.3595881547881054548+0.2887445150054544593*I:67
11:0.6425885882114633570+0.1166663566019003847*I:208
12:2.878299172613167593-3.207146978663297539*I:617
13:0.1244347803915654072+0.02554635416599550040*I:1642
14:7.335114079703045237+3.242496037410727459*I:4753
15:0.2342154484667284500+0.3944681641239107633*I:12549
  *** zeta: Warning: increasing stack size to 16000000.
16:0.4044868025470101147+3.673960915892858620*I:31561
  *** zeta: Warning: increasing stack size to 32000000.
17:0.01519449085215135598+0.2732992070062236151*I:91830
18:-0.1290841504928400845-0.1390444692970102558*I:264075
  *** zeta: Warning: increasing stack size to 64000000.
19:25.97144266877496180+11.16653934324971433*I:776618
  *** zeta: Warning: increasing stack size to 128000000.
20:-0.2955212626260033349+3.332130481547672170*I:2417687
  *** zeta: Warning: increasing stack size to 256000000.
21:1.918864622208125892-1.769834251775985217*I:7844483
  *** zeta: Warning: increasing stack size to 512000000.
22:1.082402089470537491-5.113791705983812334*I:26495868

Cheers,
Bill.